TABLES 


FINDING  THE   STRAINS 


RAILWAY  BRIDGE  TRUSSES 

UNDER  THE  ACTION  OF  A 

CONCENTRATED   LOAD  SYSTEM. 

• 
- 

REPRINTED   FROM   STRAINS   IN    FRAMED   STRUCTURES. 

SECOND     EDITION. 


BY 

A.   J.    DUBOIS, 

PROFESSOR  OF  CIVIL  ENGINEERING  IN  SHEFFIELD  SCIENTIFIC  SCHOOL  OF  YALE  COLLEGE. 


NEW   YORK : 

JOHN     WILEY     &     SONS, 

15    ASTOR   PLACE. 

1885. 


COPYRIGHT,  1883, 
BY  JOHN  WILEY  &  SONS. 

s 


u? 

-v 

& 


PREFACE. 


THESE  Tables  are  intended  to  aid  those  engaged  in  the  calculation  of  trusses.  The 
system  of  concentrated  loads  annexed,  is  very  closely  that  generally  laid  down  in  the 
specifications  of  our  principal  railroads.  The  use  of  the  tables  will  be  found  sufficiently 
illustrated  for  all  those  for  whom  they  are  designed.  The  principles  upon  which  the 
calculations  are  based  are  given  at  length  in  the  author's  work,  "Strains  in  Framed 
Structures''  from  which  these  Tables  are  reprinted. 

December  10,  1884. 


TABLE    I. 


CONCENTRATED    LOAD    SYSTEM. 


SHEAR. 


UNIVERSITY 


TABLE    I. 


CONCENTRATED   LOAD   SYSTEM. 
SHEAR. 


EXPLANATION  OF  TABLE. 

THE  load-system  adopted  is  given  in  Table  I.  It  consists  of  two  locomotives  with  tenders,  followed  by 
train  ;  the  wheel-weights  and  distances  being  given  in  the  first  column.  The  locomotive  agrees  closely  with 
the  "  standard  consolidated  engine,"  usually  specified  by  the  best  railroad  and  bridge  companies.  It  is  believed 
that  the  load-system  assumed  is  such  as  will  give,  in  every  case,  results  slightly  in  excess  of  the  heaviest  possi- 
ble loading  which  can  actually  occur  in  practice. 

The  use  of  Table  I.  is  quite  simple.  The  length  of  span  is  /.  The  load  always  comes  on  from  right, 
The  maximum  shear  at  any  point,  distant  x  from  the  left  end,  is  given  by  one  of  four  formulas.  These  formulae, 
and  the  limits  between  which  they  hold  good,  are  given  at  the  head  of  the  table.  For  \\\<t  first  eight  feet  of  any 
span  we  must  use  formula  (I.).  From  x  —  8  up  to  a  certain  limit  we  must  use  (II.).  This  limit  is  given  in  the 
table  to  right,  for  every  length  of  span  from  27  to  300.  Thus,  for  a  span  of  100  feet,  this  limit  is  47^  feet  from 
the  left  end.  From  this  limit,  up  to  x  —I  —  8,  we  must  use  formula  (III.).  At  the  limit,  both  (II.)  and  (III.) 
give  the  same  result.  For  the  last  eight  feet  of  span  we  use  formula  (IV.). 

Thus,  for  instance,  for  a  span  of  200  feet,  we  must  use  (I.)  from  x  —  o  up  to  x  =  8.  From  x  =  8  up  to 
x  =  89^  we  must  use  (II.).  From  *  =  89^  up  to  x  =  192  we  must  use  (III.).  From  x  =  192  up  to  x  =  200  we 
must  use  (IV.). 

The  table  gives  the  values  of  P  and  A  for  the  corresponding  value  oil  —  x,  or  /  —  x  —  8. 

Thus,  suppose  ive  -wish  the  maximum  shear  for  a  span  of  200  feet,  at  7,  80,  loo,  and  195  feet  from  end, 
load  coming  on  always  from  right. 

For  x=  7  we  use  formula  (I.).  We  have,  then,  /=  200,  /—  x=  193.  From  table,  we  see  that  for  any 
value  of  /—  x  between  190  and  195  we  have  P  —  527000,  and  A  =  41730000.  Hence,  for  x=  7, 

527000  41730000 

Shear  =  —  —  193  —  ^-^  --  =  299905  Ibs. 
200  200 

In  like  manner,  for  x=8o,  we  have  I—  x  =  120,  /—  x  +  8  =  128;  and,  since  the  limit  is  89^,  we  must  use 
formula  (II.).  We  have  from  table,  for  /  —  x  =  120,  P  —  383000,  and  A  =  19410000;  and,  hence, 

15000  383000  10410000 

Shear  =-   —  128  +  ^-^—120  --  =          --  15000=127350^5. 
200  200  200 

Observe  that  the  table  gives  these  values  of  P  and  A  for  any  value  of  /  —  x  between  r  1  5  and  120,  including 
1  20.  For  any  value  of  /  —  x  between  120  and  125,  including  120,  we  have,  also,  P  —  395000,  A  —  20850000; 
and  these  values  in  formula  (II.)  would  give  the  same  result.  Thus, 

15000     „      395000  20850000 

Shear  =  —  -  128  +  —  —  120  ---         --  15000  =  127350  Ibs. 

200  200  200 

For  x=  100,  we  have  I—  x—  100,  /—  x  —  8  =  92;  and,  since  the  limit  is  89^,  we  must  use  formula  (III.). 
We  have  from  table,  for  /—  x  —  8  =  92,  P  =  335000.  A  =  14370000  ;  and,  hence, 

15000  335000          14370000 

Shear  =  -=  —  100  +  ===  —  -92  --  ^-    —  —  89750  Ibs. 
200  200   '  200 

For  x  =  195,  since  this  falls  within  the  last  8  feet,  we  must  use  formula  (IV.).  We  have,  then,  /  —  x  =  5  ; 
and 


Shear  =  5  =  375  Ibs. 

2OO 

Whenever  formula?  (I.)  or  (II.)  apply,  the  second  wheel  is  at  the  point:  when  (III.)  or  (IV.)  apply,  the  first 
wheel  is  at  the  point. 


TABLE    I. 


UNIVERSITY 


CONCENTRATED   LOAD   SYSTEM. 
SHEAR. 

/  =  length  of  span. 

x  =  distance  from  left  end,  in  feet,  of  any  point  at  which  the  maximum  shear  is  required. 

Values  of  P  and  A  to  be  taken  from  table  for  corresponding  /  —  x,  or  /  —  x  —  8. 


From  x  =•  o  to  x  =  %,      )     .  P  .  A 

j     i    ,    ,  j.  •  *  /Shear  =  -7(/  —  x)  --  r- 
second  wheel  at  point,  |  /  / 

From  x  =  %>  to  limit,       \    .  pi.. 

>Shear  =  M/— 


,  \ 
.,  > 
int,  \ 


0       /* 

8)+  -( 
I 


.,     7     »    ,,., 
second  wheel  at  point,  \  I 

Limit  to  be  found  from  table  on  right,  pi  —  15000. 


. 

--  r  —  15000. 
I 


(II.) 


(III.) 


From  x  =  limit  to  x  —  I  —  8, 
first  wheel  at  point, 


Shear  =  ^-' (/—*)  +  -=•(/  —  x  —  8) r 

I  I  I 

"row  x  —  I  —  8  to  x  •• 
first  wheel  at  point, 


From  x  —  I  —  8  to  x—  /, )  „,  /i , . 

\  Shear  =  fj  (I  —  x). 


(IV.) 


WEIGHTS,  LBS. 

Distances. 

I-* 

or 
l-x-8. 

p 

A 

WEIGHTS,  LBS, 

Distances.  | 

/-.r 
or 
i-x-S. 

P 

A 

Span. 

Limit 

Span. 

Limit. 

feet 

x. 

feet. 

x. 

,  /,  =15000 

ft. 

—  I  

/I8  =  1  5000 

ft. 

9' 

•  8 

4 

335000 

14370000 

27 

1  8.6 

6l 

38.5 

a 

/2   =  25000  j 

O 

/„=  12000 

95 

28 

'9 

62 

39i 

5 

25000 

O 

1 

5 

347000 

15510000 

29 

19.4 

63 

39f 

2  J  /3  =  25°°° 

5 

, 

/20=  12000 

IOO 

3° 

19.9 

64 

39i 

SI 

5 

50000 

125000 

rt 

10 

359000 

16710000 

31 

2O.6 

65 

39i 

O 

/4  =  25000 

10 

^ 

/2I=  12000 

no 

32 

21-3 

66 

39i 

J 

5 

75000 

375000 

5 

371000 

18030000 

33 

22 

67 

39| 

fs  =  25000 

15 

pa=  12000 

"5 

34 

227 

68 

^ 

7 

100000 

750000 

5 

383000 

19410000 

35 

234 

69 

40?, 

pf,  —  15000 

22 

/23  =  I  2000 

r  20 

36 

24.1 

70 

4'i 

5 

115000 

1080000 

5 

395000 

20850000 

24.8 

7' 

415 

0) 

/,  =  15000 

27 

/24  =  1  2OOO 

125 

38 

25.5 

72 

42j 

*3 

c  • 

5 

130000 

1-485000 

rt 

IO 

407000 

22350000 

39 

26.2 

73 

4*1 

OJ 

p,  —  1  5000 

32 

w 

p25  =  12000 

"35 

40 

26.8 

74 

42i 

'  5 

145000 

1965000 

5 

419000 

23970000 

4' 

27.2 

75 

425 

/,  =  15000 

37 

p26  —  !  2°O° 

140 

42 

276 

76 

43i 

*  *       •* 

•  9 

160000 

2520000 

5 

431000 

25650000 

43 

28 

77 

433 

/io=  15000 

46 

/27=  T2000 

'45 

44 

S87 

78 

44i 

§ 

;  8 

175000 

3210000 

5 

443000 

27390000 

45 

29.4 

79 

445 

Q 

/„  =  25000 

•  5 

54 

20OOOO 

^560000 

rt  • 

/28  =  I  2000 

IO 

150 

455000 

29190008 

46 

47 

30.1 
30.8 

80 
Si 

45i 
45i 

E 

/12  =  25000 

11 

59 

O 

/2,  =  I  2000 

1  60 

48 

3'-5 

82 

8 

5 

225000 

6035000 

5 

467000 

3IIIOOOO 

49 

32.2 

83 

4li 

J3 

/>,3  =  25OOO 

64 

/jo  =  I  2OOO 

" 

165 

50 

329 

84 

»—  i 

5 

250000 

7635000 

5 

479000 

33090000 

51 

33-6 

85 

463 

/14  =  25000 

69 

/3I  =  12000 

170 

52 

34-3 

86 

47  i 

7 

275000 

9360000 

5 

491000 

35130000 

53 

35 

87 

4Zl 

/„=  15000 

76 

/32  =  I  2000 

175 

54 

35-4 

88 

4**H 

u 

5 

/I6=  15000  j 

81 

290000 

10500000 

rt 
O 

/33=  12000 

IO 

185 

503000 

37230000 

55 
56 

1 

89 
90 

4^ 

c 

•  s 

305000 

11715000 

5 

515000 

39450000 

57 

36.6 

91 

48  i 

r* 

/„  =  15000 

86 

/„=  12000 

190 

58 

37 

92 

48! 

•  5 

320000 

13005000 

5 

527000 

41730000 

59 

37-4 

93 

48  1 

/„  =  15000 

91 

^35  —  liUUU 

'95 

60 

375 

94 

47i 

TABLE    I. 


CONCENTRATED   LOAD   SYSTEM. 
SHEAR. 

/  =  length  of  span. 

x  =  distance  from  left  end,  in  feet,  of  any  point  at  which  the  maximum  shear  is  required. 

Values  of  P  and  A  to  be  taken  from  table  for  corresponding  /  —  x,  or  /  —  x  —  8. 


From  x  —  o  to  x  —  8,      I 

(I.)  ,     .     .    .  ,   .  '     > 

second  wheel  at  point,} 


, 
Shear  =  -j(l—x)  --  r 


From  x  =8  to  limit,       \  „.  pi,,  a.       P.,  A 

,     ,     ,    J,   .      >  Shear  =  ~(l  —  x+  8)  +  -=•(/  —  x)  --  r  —  15000.         (II.) 
second  -wheel  at  point,  \  /v  .  /  / 

Limit  to  be  found  from  table  on  right,  pi  =  15000. 

from  x  =  limit  to  x  =  /  —  8.  |  _,  pi.,  P  ,  0.       A 

(HI-)  first  -wheel  at  point,  }Shear  =  T(/~  x)  +  7(/~  *  ~  8)  ~  T 

From  x=i-Stox  =  I,  )  _  /. 

first  wheel  at  point,        \  bhear  °  ~J(l      x>~ 


WEIGHTS,  LBS. 

Distances 

/-  X 

or 

/--  r-8. 

P 

A 

Span, 
feet. 

Limit. 

Span. 

Limit. 

Span. 

Limit. 

Span. 
feet. 

Limit. 

Span. 

Limit, 

Span. 

Limit. 

x. 

feet. 

x. 

feet. 

x. 

x* 

feet. 

x. 

feet. 

x. 

#„  —  12000 

f, 

'95 

/36  =  I  2OOO 

s 

2OO 

539000 

44070000 

1 

47* 
473 

128 
129 

62.5 
63.2 

161 

162 

79. 

79: 

194 

9'B 

£2n 

227 
228 

89ft 
89i 

260 
261 

9'i 
9'ft 

u 

10 

551000 

46470000 

47i 

'3° 

639 

"63 

80) 

196 

923 

229 

89ft 

262 

9'  ft 

O 

Py,—  12000 

2IO 

98 

471 

64.6 

164 

80: 

"97 

92I*z 

230 

89ft 

263 

9'i! 

5 

563000 

48990000 

99 

47  i 

132 

65-3 

I65 

81: 

198 

9'l 

23' 

89!! 

264 

/3a  —  1  2000 

215 

100 

474 

'33 

66 

1  66 

81: 

- 

199 

9'  ft 

232 

9°J 

265 

92!} 

5 

575000 

51570000 

IOI 

474 

'34 

66.4 

167 

Si 

200 

89i 

233 

9°zi 

266 

92I 

pyi  =•  I2OOO 

22O 

1  02 

47.6 

'35 

66.8 

168 

81; 

20  1 

234 

9°f 

267 

92ft 

•   S 

587000 

54210000 

103 

48 

136 

67.2 

169 

82 

2O2 

88| 

235 

9°ft 

268 

92I 

\ 

/40  —  1  2OOO 

225 

104 

48.4 

'37 

67.8 

170 

82; 

2O3 

88ft 

236 

9°l 

269 

93?? 

d 

•10 

599000 

56910000 

105 

48.8 

138 

68.5 

17' 

83: 

2O4 

88| 

237 

9'uV 

270 

93fz 

(J 

/4l  =  I  20OO 

235 

106 

49.2 

'39 

69.2' 

172 

8^ 

205 

89?^ 

238 

91  ?? 

271 

93z  I 

•   S 

6lIOOO 

59730000 

107 

49.6 

140 

69.9 

'73 

84] 

206 

89ft 

239 

272 

94  \ 

/«  =  1  20OO 

240 

108 

5° 

141 

70.6 

'74 

84: 

207 

9°T2 

240 

9"i 

273 

94ft 

• 

/43  =   12000 

'   5 

245 

623000 

62610000 

109 

IIO 

50.4 
50.9 

142 
'43 

7i-3 

72 

'75 
176 

84  : 
84! 

208 
209 

9^1*2 

241 

242 

92ft 

9'  H 

274 

275 

93l, 
93ft 

'    5 

635000 

65550000 

in 

516 

144 

72-7 

'77 

85: 

- 

210 

»9H 

243 

92A 

276 

93s 

/«4  =  12000 

250 

112 

52-3 

MS 

73-4 

178 

85; 

211 

9OzV 

244 

92i 

277 

9jft 

IO 

647000 

68550000 

"3 

53 

146 

74.1 

179 

86 

212 

9°i 

245 

93?* 

280 

rt   . 

CJ 

/4S  =  12000 

260. 

114 

53-7 

M7 

74.6 

1  80 

86; 

2I3 

9^2f 

246 

93?5 

281 

9°il 

c 

659000 

71670000 

"5 

54-4 

148 

75 

181 

87: 

214 

9'ft 

247 

93ft 

285 

92jV 

/46  =  12000 

265 

n6 

55-  ' 

149 

75-4 

182 

87; 

215 

9'ft 

248 

93J 

286 

9'l 

S 

67IOOO 

74850000 

117 

55-8 

150 

75-8 

"83 

5 

216 

9'i 

249 

93ft 

287 

9'Jf 

/47  =  12000 

270 

n8 

'5' 

76.2 

184 

88^ 

V 

217 

250 

92| 

291 

93  A 

s 

683000 

78090000 

119 

57.2 

152 

76.6 

185 

88J 

\ 

218 

9'8 

251 

9°ft 

292 

934 

/,8  =  t2OOO 

275 

1  20 

57.8 

'53 

77 

1  86 

89, 

V 

219 

92^1 

'252 

9°3 

293 

93ft 

U 

•10 

695000 

81390000 

121 

58.2 

"54 

77-4 

187 

893 

f 

2  2O 

253 

9°ft 

294 

93f? 

u  ' 

/4,  =  12000 

>   S 

285 

707000 

84810000 

122 
I23 

58.6 
59 

'55 
"56 

781 

188 
189 

90, 

goJ 

I 

221 

222 

92^ 

254 
255 

m 

296 

94J 

/so  =  12000 

•s 

290 

719000 

88290000 

124 
125 

60.4 

'57 
158 

7ft 

78| 

190 
191 

90, 
90 

• 

1 

223 
224 

W 

256 

257 

& 

297 
298 

94  s 

/SI  =  I  2000 

295 

I2O 

61.1 

"59 

192 

9' 

225 

92ft 

258 

9°ii 

299 

94A 

5 

731000 

91830000 

127 

61.8 

160 

78| 

"93 

9'i 

1 

226 

89! 

259 

9'?¥ 

300 

/S2  =  1  2OOO 

300 

TABLE   II. 


CONCENTRATED    LOAD    SYSTEM. 


*  In  applying  II.  to  a.  framed  girder,  if  the  panel  length  is  more  than  8  feet,  we  must  put  instead  of    15000  (=  pi), 
that  portion  of  pi  only,  which,  by  the  law  of  the  lever,  takes  effect  at  the  1st  apex  on  left  of  pi. 


TABLE   I. 


(i.) 


CONCENTRATED    LOAD   SYSTEM. 
SHEAR. 

/  =  length  of  span. 

x  =  distance  from  left  end,  in  feet,  of  any  point  at  which  the  maximum  shear  is  required. 

Values  of  P  and  A  to  be  taken  from  table  for  corresponding  /  —  x,  or  /  —  x  —  8. 


From  x  =  o  to  x  =  8, 
second  wheel  at  point, 

From  x  =  8  to  limit,       \ 


fa 

=  —- 


rom  x  =       o    m,         „.  .,  ...  ., 

j     ,     ,    *  +  •  +  >  Shear  =  —-(/—  x+  8)  4-  -r(/—  x)  --  r  —  15000. 
second  wheel  at  point,  \  /  .  /  / 

Limit  to  be  found  from  table  on  right,  /i  =  15000. 


(II.) 


From  x  —  limit  to  x  =  I  —  8,  |  „,  fa  . 

first  wheel  at  point,  |  Shear  =-(/_. 


From  x  =  I  —  8  to  x  =  /, 

,     ..... 
first  wheel  at  point, 


x  =  /,  |  _,  fa  . 

..        >  Shear  =  T-(/—  x). 
int,        \  I* 


(IV.) 


WEIGHTS,  LBS. 

Distances 

/-  x 
or 
t-x-1. 

P 

A 

Span. 

Limit. 

Span. 

Limit. 

Span 

Limit. 

Span, 
feet. 

Limit 

Span. 

Limit. 

Span. 

Limit. 

feel. 

x. 

feet. 

x. 

feet. 

x. 

X. 

feet. 

x. 

feet 

x. 

TABLE   II. 


CONCENTRATED    LOAD    SYSTEM. 


MOMENTS. 


TABLE   II. 


CONCENTRATED   LOAD   SYSTEM. 
MOMENTS. 


EXPLANATION  OF  TABLE. 

FOR  the  maximum  moment  at  any  point  of  any  span  given  in  the  table,  simply  multiply  the  value  of  the 
reaction  Jf  by  the  value  of  x,  the  distance  of  point  from  the  left  end,  and  subtract  the  value  of  /«.  The  index 
of  p,  in  the  last  column,  shows  the  number  of  the  wheel  which  must  rest  on  the  point,  and  hence  the  position  of 
the  load-system  on  the  span.  The  load-system  itself  is  given  in  Table  I. 

Thus,  for  span  of  200  feet :  — 

At  5  feet  from  left  end,  the  reaction  at  left  end  is  R  —  305175  Ibs.    The  moment  is 
Kx=  305 1 75  x  5=  1525875- 

The  second  wheel  of  the  system  must  rest  on  the  point. 

At  10  feet  from  left,  the  reaction  is  j?  =  306850  Ibs.    The  moment  is 

fix  —  m  =  306850  x  10  —  120000  =  2948500. 

The  second  wheel  of  the  system  must  rest  on  the  point. 

At  20  feet  from  left,  the  reaction  is  J?  =  293600  Ibs.     The  moment  is 

Rx  —  m  =  293600  x  20  —  320000  =  5552000. 
The  third  wheel  of  the  system  must  rest  on  the  point. 

To  find  the  moment  at  a  point  not  given  by  the  table,  find  the  reaction  R  for  this  point  by  interpolation, 
and  then  proceed  as  before.  Thus, 

At  30.7  feet  from  left,  the  reaction  is  280650  —  (280650  —  278060)3*5  =  278837.    The  moment  is 

Rx  —  m  —  278837  x  30.7  —  645000  =  791520. 
The  fourth  wheel  of  the  system  must  rest  on  the  point. 

If,  however,  this  point  falls  between  two  "fields"  find  the  moment  by  interpolation.    Thus, 

At  45.4  feet  from  left,  we  have  the  moment  at  45,  255050  x  45  —  1095000  —  10382250.    The  moment  at  46 
-is  270290  x  46  —  1900000  =  10533340.    At  45.4,  then,  we  have 

10382250  +  (10533340—  10382250)^,  =  10442686. 
The  fifth  or  sixth  wheel  at  point,  indifferently. 

In  general,  it  will  not  be  necessary  to  interpolate,  but  will  be  sufficient  to  take  the  nearest  foot  given  in 
the  table. 

To  find  the  moment  at  any  point  of  a  span  not  given  in  the  table,  find  the  moment  at  the  same  point  for 
the  two  nearest  spans  given,  and  interpolate. 

Thus,  span  204  feet,  moment  at  10  feet  from  left:  — 

The  moment  at  10  feet  from  left,  for  a  span  of  200  feet,  is  2948500.  The  moment  at  10  feet  from  left,  for 
span  of  210  feet,  is  3063330.  The  moment  at  10  feet  from  left,  for  204  feet  span,  is,  then, 

2948500  +  (3063330  -  2948500)  1%  =  2994432. 
The  second  wheel  of  system  at  point, 
vi 


TABLE     II. 


CONCENTRATED    LOAD    SYSTEM. 
MOMENTS. 


=  J?x  — 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

10 

ii 

12 

13 

feet. 

feet. 

feet. 

feet. 

JC 

y? 

m 

X 

^ 

m 

.r 

j? 

m 

X 

i? 

m 

I 

32500 

I 

34090 

I 

375oo 

I 

40384 

2 

3 

2/500 
22500 

o 

A 

2 

3 

29545 
25000 

{>•, 

2 

3 

31250 
27083 

0 

P* 

2 

3 

34615 
28846 

0 

A 

4 

17500 

4 

20454 

4 

22916 

4 

25000 

5 

12500 

5 

25909 

S 

18750 

S 

2»53 

6 

21363 

6 

37500 

ri 

Pi 

6 

7 

40384 
346i5 

IO 
N 

A 

1  " 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

M 

'5 

16 

>7 

feet. 

feet. 

feet. 

feet. 

JC 

K 

m 

X 

R 

in 

AT 

R 

m 

jr 

K 

m 

I 

42857 

, 

45000 

I 

46875 

T 

50000 

2 

375°° 

T 

40000 

2 

42187 

2 

44117 

3 

32142 

0 

A 

3 

35000 

o 

A 

3 

37500 

o 

f, 

3 

39705 

o 

A 

4 

26785 

4 

30000 

4 

32812 

4 

35Z94 

5 

23214 

5 

25000 

5 

28125 

5 

30882 

6 

7 

42857 
37500 

1^1 

N 

A 

6 

8 

45000 
40000 
35000 

PI 

A 

6 

8 

46875 
42187 
37500 

N 

ft 

6 

8 

50000 
44117 
39705 

w> 
fl 

/. 

9 

35294 

Vlll 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

18 

19 

20 

21 

feet. 

feet. 

feet. 

feet. 

X 

y? 

m 

^ 

y? 

m 

X 

R 

m 

X 

* 

in 

i 

52777 

i 

55263 

\ 

57500 

i 

59523 

2 

3 

47222 
41666 

o 

A 

2 

3 

5OOOO 
44736 

o 

P* 

2 

3 

52500 
47500 

o 

* 

2 

3 

54761 
50000 

o 

/» 

4 

37500 

4 

39473 

4 

42500 

4 

45238 

5 

33333 

5 

35526 

5 

37500 

5 

40476 

6 

52777 

6 

55263 

6 

57500 

6 

59523 

I 

47222 
41666 

1 

Pi 

8 

50000 
44736 

8, 

P, 

21 

52500 
47500 

8 

h 

8 

54761 
50000 

8 

9 

37500 

9 

10 

39473 
35526 

9 

10 

42500 
37500 

~ 

9 

10 

45238 
40476 

N 

ti 

ii 

357H 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

22 

23 

24 

25 

feet. 

feet. 

feet. 

feet. 

.r 

/? 

. 

* 

R 

m 

X 

R 

m 

X 

R 

m 

I 

61363 

i 

63043 

i 

65208 

i 

67200 

2 

56818 

2 

58695 

2 

60416 

2 

62600 

3 

52272 

o 

A 

3 

54847 

O 

P> 

3 

56250 

o 

P* 

3 

58000 

o 

P* 

4 
5 

47727 
43181 

4 
5 

50000 
45652 

4 
5 

52083 
47915 

4 

5 

54000 
50000 

1 

6 

61363 

6 

63043 

6 

65208 

6 

67200 

7 

56818 

7 

58695 

7 

60416 

7 

62600 

8 

52272 

8 

8 

8 

56250 

8 

8 

58000 

Q 

9 
10 
ii 

47727 
43181 
38636 

N 

9 
10 
ii 

50000 
45652 
41304 

ft 

n 

Pi 

9 
10 
it 

52083 
479  '5 
43749 

M 

Pi 

9 

10 

ii 

54000 
50000 
46000 

N 

M 

ti 

12 

36956 

12 

39582 

12 

42000 

13 

38000 

• 

CONCENTRATED  LOAD  SYSTEM. 


IX 


MOMENTS. 


M.,  —  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

26 

27 

28 

29 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

* 

R 

m 

x 

R 

m 

.*• 

A' 

m 

i 

69038 

i 

70740 

i 

72321 

i 

74306 

2 

64615 

2 

66481 

2 

68213 

2 

69820 

3 
4 

60192 
55769 

o 

A 

3 
4 

62222 
57962 

o 

A 

3 

4 

64106 
60000 

o 

A 

3 
4 

65855 
61889 

O 

A 

5 

5  '923 

5 

53703 

5 

55891 

5 

57924 

6 

50000 

6 

5  '783 

6 

53958 

6 

69038 



7 

64615 

7 

66481 

7 

68213 

7 

69820 

8 
9 

60192 
55769 

8 

8 
9 

62222 
57962 

g 

8 
9 

64106 
60000 

R 

8 

65855 
61889 

g 

10 
1  1 

51923 
48076 

2 

Pi 

IO 

II 

53703 
50000 

10 
M 

A 

10 

ii 

5589' 
51783 

8, 

CI 

M 

/3 

IO 

ii 

57924 
5395s 

10 
N 

/3 

12 

44230 

12 

46296 

12 

48212 

12 

49993 

13 

40384 

13 

42592 

>3 

44640 

«3 

46544 

"4 

53333 

1 

A 

M 

55533 

CO 

/3 

14 

15 

57578 
53612 

cr 

/>3 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

3° 

31 

32 

33 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

JC 

R 

m 

' 

R 

m 

X 

R 

,„ 

, 

76166 

i 

77903 

I 

79531 

i 

81060 

2 

71833 

2 

73709 

2 

75468 

2 

77121 

3 
4 

67500 
63666 

o 

A 

3 
4 

69516 

65322 

o 

A 

3 

4 

71406 
67343 

o 

A 

3 

4 

69242 

o 

A. 

1 

56000 

* 

61612 
57903 

* 

63281 
59687 

I 

65303 
61363 

. 

71833 

7 

73709 

7 

75468 

7 

77121 

8 

67500 

8 

69516 

8 

71406 

8 

9 

IO 

ii 

63666 

59833 
56000 

N 

A 

9 

IO 

ii 

65322 
61612 

57903 

N 

M 

A 

9 

IO 

ii 

67343 
63281 

59687 

N 

/3 

9 

10 

ii 

69242 

65303 
61363 

1 

/3 

12 

52166 

12 

54193 

12 

56093 

12 

57878 

'3 

48333 

'3 

50483 

»3 

52500 

'3 

54393 

14 
IS 

59500 
55666 

CO 

A 

14 

61290 
53870 

1 

A 

'4 

15 
16 

63436 
•   59373 
5578o 

H 

/3 

M 
15 
16 

65454 
61514 

57574 

N 

/>3 

i? 

54090 

APPENDIX. 


MOMENTS. 


/r  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

34 

35 

36 

37 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

jr 

R 

m 

X 

R 

m 

JC 

R 

m 

I 

82941 

I 

84714 

I 

86388 

1 

87972 

2 

3 
4 

78676 

74852 
71029 

o 

p* 

2 

3 
4 

80571 
76428 
72714 

o 

A 

2 

3 
4 

82361 
78333 
74305 

0 

/* 

3 
4 

84054 
80135 
76216 

o 

A 

\ 

67205 

63382 

0 

69000 
65285 

^ 

70694 
67083 

72297 
68702 

8 

78676 
74852 

I 

80571 
76428 

7 

82361 
78333 

§ 

84054 
80135 

9 

71029 

§ 

9 

72714 

8 

9 

74305 

S 

9 

76216 

X 

to 

67205 

§1 

fit 

IO 

69000 

Si 

P* 

IO 

70694 

LO 

/>< 

IO 

72297 

& 

/3 

ii 

63382 

N 

II 

65285 

ii 

67083 

N 

ii 

68702 

N 

12 

'3 

59558 

56176 

12 

'3 

61571 
57857 

12 
'3 

63472 
5986i 

12 
'3 

65108 
6I5I3 

14 

67353 

14 

69143 

M 

70833 

14 

725'3 

16 

i? 

63528 

59705 
55822 

n 
n 

/3 

>5 
16 

!I 

65428 
61714 
58000 
54286 

w 

to 

/3 

15 

ID 

17 

18 

67221 
63611 
60000 
563^8 

N 

n 

/3 

:i 

"7 

18 

68512 
65000 
61486 
57937 

fj 

m 

/3 

'9 

54460 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

38 

38 

39 

39 

feet. 

feet. 

feet. 

feet. 

jr 

R 

m 

X 

R 

I/I 

jr 

R 

m 

X 

R 

m 

I 

89473 

14 

74737 

I 

91282 

14 

76538 

2 

85657 

15 

70921 

§ 

2 

87179 

15 

72819 

§ 

3 

4 

81842 
78027 

o 

P* 

16 

'7 

67105 
63685 

PI 
ro 

/3 

3 

4 

83461 
79743 

o 

A 

17 

69102 
65384 

w 

fO 

/3 

5 

74211 

18 

60263 

76025 

18 

62050 

6 

70395 

6 

72307 

19 

74737 

§ 

^4 

19 

76538 

»-n 

A 

7 

85657 

7 

87179 

8 

81842 

v?T 

8 

83461 

^ 

9 

78027 

§ 

9 

79743 

§ 

10 

74211 

Wl 

ft 

IO 

76025 

v~> 

A, 

ii 

70395 

II 

72307 

12 

66974 

12 

68589 

'3 

63553 

'3 

65256 

CONCENTRATED   LOAD  SYSTEM. 


•  XI 


MOMENTS. 


M,,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

40 

41 

42 

43 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

J? 

m 

X 

R 

m 

X 

J? 

m 

I 

93000 

I 

94634 

i 

96190 

I 

97674 

2 

89000 

2 

90731 

2 

92380 

2 

93953 

3 

4 

85000 
8i375 

o 

A 

3 
4 

86829 
82926 

0 

A 

3 
4 

88571 
84761 

0 

A 

3 

4 

90232 
86511 

o 

A 

7775° 

S 

79390 

80952 

82790 

6 

74125 

6 

75853 

6 

77500 

6 

79069 

7 

89000 

7 

90731 

7 

92380 

7 

93953 

8 

85000 

8 

86829 

8 

88571 

8 

90232 

9 

81375 

g 

9 

82926 

8 

9 

84761 

g 

9 

86511 

9 

10 

7775° 

"•) 

ft 

10 

79390 

»o 

ft 

10 

80952 

to 

ft 

10 

82790 

*n 

A 

ii 

74125 

ii 

75853 

ii 

77500 

ii 

79069 

12 

70500 

12 

72317 

12 

74047 

12 

75697 

£3 

66875 

13 

68780 

«3 

7059S 

'3 

72325 

14 

78250 

14 

79877 

14 

81784 

H 

83604 

9 

74625 
71000 

A 

15 

1  6 

76341 
72804 

§ 

ft 

15 
16 

77975 
74523 

jj 

ft 

J| 

79883 
76162 

§ 

A 

17 

67375 

ro 

17 

69267 

n 

fO 

17 

71071 

ro 

17 

72790 

H 
CO 

18 

65730 

18 

67618 

18 

69417 

18 

81875 

g 

'9 

78250 

"-> 

A 

19 

79S77 

g 

19 

81784 

g 

19 

83604 

g 

20 

74625 

* 

20 
21 

76341 
72§04 

"i 

<3" 

A 

20 

21 

77975 
74523 

ft 

v? 

A 

20 

21 

79883 
76162 

*T1 

J? 

A 

22 

72790 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

44 

44 

45 

45 

feet. 

feet. 

feet. 

feet. 

X 

R 

in 

X 

R 

m 

X 

R 

« 

X 

R 

OT 

, 

99090 

M 

85340 

I 

100444 

14 

87000 

2 

95454 

15 

81704 

S 

2 

96888 

83444 

§ 

3 

4 
5 

91818 
88181 
84545 

O 

A 

10 

17 
18 

78067 
7443  ' 
7H35 

N 

m 

A 

3 
4 

93333 
89777 
86222 

0 

A 

ii 

80000 
76333 
72777 

Cl 

rt 

A 

6 

80909 

6 

82666 

7 

79111 

19 

85340 

iq 

87000 

7 

95454 

20 

81704 

g 

20 

83444 

g 

8 

91818 

21 

78067 

•*!- 

A 

8 

93333 

21 

80000 

>o 

A 

9 

88181 

g 

^•J 

7443' 

vo 

9 

89777 

_ 

22 

76333 

v?r 

10 

84545 

"i 

ft 

10 

86222 

§ 

23 

72777 

ii 

80909 

£! 

ii 

82666 

to 

M 

3 

12 

77272 

12 

79111 

*" 

'3 

73977 

13 

75555 

Xll 


APPENDIX. 


MOMENTS. 


M,.  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

46 

47 

48 

49 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

R 

1 

m 

X 

/? 

m 

X 

R 

m 

i 

101739 

I 

102978 

i 

104479 

i 

105918 

2 

98260 

2 

99574 

2 

100834 

2 

102346 

3 

94782 

T 

96170 

3 

975°o 

3 

98775 

4 

91304 

0 

P* 

4 

92765 

o 

P* 

4 

94166 

o 

A 

4 

955°9 

o 

ft 

3 

7 

87826 

84347 
80869 

7 

89361 
85957 
82553 

7 

90833 
87500 
84166 

7 

92244 
88978 
85712 

8 

94782 

8 

96170 

8 

97500 

8 

98775 

9 

91304 

Q 

9 

92765 

o 

9 

94166 

o 

9 

95509 

Q 

10 
n 

87826 
84347 

w 

ft 

10 
ii 

89361 
85957 

10 
« 

ft 

10 
ii 

90833 
87500 

N 

f» 

10 
ii 

92244 
88978 

to 

M 

ft 

12 

80869 

" 

12 

82553 

12 

84166 

•"• 

12 

85712 

1-1 

13 

77391 

'3 

79148 

13 

80833 

13 

82446 

14 

88586 

14 

90424 

'4 

92187 

'4 

93874 

15 

85107 

Q 

15 

86701 

Q 

15 

88541 

g 

IS 

90302 

g 

ID 
17 

18 

81629 
78151 
74673 

rt 
f> 

ft 

16 

17 
18 

83297 

8> 

Ps 

16 

i? 
18 

84895 
81563 
78229 

Cl 

n 

pi 

16 

17 
18 

86729 
83T59 
79893 

N 
fO 

Pi 

'9 

88586 

19 

90424 

19 

92187 

19 

93874 

20 

21 
22 
23 

85107 
81629 
78151 
74673 

tO 

^ 

p4 

20 

21 

22 

23 
24 

86701 
83297 
79893 
76489 

73085 

<^- 

vo 

A 

20 

21 
22 
23 
24 

88541 
84895 
81563 
78229 
74896 

£ 

A 

20 

21 
22 
23 
24 

90302 
86729 
83159 

79893 
76628 

»o 

^ 

P4 

25 

73363 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

5° 

5° 

51 

Si 

feet. 

feet. 

feet. 

feet. 

jr 

J? 

m 

X 

R 

m 

X 

R 

m 

X 

R 

m 

I 

107300 

14 

95500 

I 

108627 

14 

97057 

2 

103800 

92000 

g 

2 

105196 

15 

93626 

g 

3 

100300 

16 

88500 

g 

i»i 

3 

101764 

16 

90195 

g 

Pi 

4 

96800 

o 

t» 

i? 

85000 

H 

n 

4 

98333 

o 

ft 

17 

86764 

ro 

93600 

18 

81500 

5 

94901 

IB 

83332 

6 

90400 

6 

91764 

7 

87200 

7 

88627 

if) 

9=1500 

19 

97057 

20 

92000 

20 

93626 

8 

100300 

21 

88500 

g 

8 

101764 

21 

90195 

9 

96800 

22 

85000 

to 

?»4 

9 

98333 

Q 

22 

86764 

t. 

10 

ii 

12 

13 

93600 
90400 
87200 
84000 

to 

M 

P* 

23 
24 
25' 

81500 
78300 
75100 

3 

10 
ii 

1  2 

"3 

94901 
91764 
88627 
8549° 

N 

ft 

23 

24 
2  C 

26 

83332 
79901 
76764 
73627 

TJ- 
VO 

CONCENTRATED  LOAD  SYSTEM. 


XIII 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

52 

53 

54 

55 

feet. 

feet. 

feet. 

feet. 

.* 

^ 

m 

AT 

R 

m 

X 

R 

m 

;r 

K 

m 

I 

109903 

, 

111132 

I 

112314 

i 

*134Sl 

2 

106538 

2 

107830 

2 

109074 

2 

110272 

3 

i°3!73 

3 

104528 

3 

105833 

3 

107090 

4 

99807 

0 

A 

4 

101226 

o 

A 

4 

102592 

0 

A 

4 

103909 

o 

A 

| 

96442 
93076 

1 

97924 
94622 

| 

99351 
96111 

1 

10x5727 
97545 

7 

90000 

7 

91320 

7 

92870 

7 

94363 

8 

I03I73 

8 

104528 

8 

I05833 

/ 

8 

107090 

9 

99807 

o 

9 

101226 

0 

9 

102592 

o 

9 

103909 

Q 

10 
ii 

96442 
93076 

u"i 

M 

A 

10 
it 

97924 
94622 

»n 

PI 

A 

10 
ii 

99351 
96111 

in 

w 

A 

10 
ii 

100727 
97545 

"1 

A 

12 

90000 

M 

12 

91320 

M 

12 

92870 

1-1 

12 

94363 

'3 

86923 

'3 

88301 

13 

89629 

13 

91181 

14 

98557 

14 

IOOOOO 

14 

101388 

14 

102727 

15 

95192 

o 

15 

96697 

g 

15 

98147 

15 

99544 

16 
17 

91826 
88461 

M 

A 

17 

93395 
90093 

N 

A 

16 
17 

94906 
91665 

§ 

ft 

16 
17 

96362 
93181 

\ 

A 

18 

85095 

<*j 

18 

86791 

fO 

18 

88425 

M 

18 

90000 

N 

'9 

81730 

19 

83489 

19 

85184 

iq 

86817 

20 

81943 

20 

83635 

20 

95'92 

20 

96697 



21 

91826 

21 

93395 

21 

94906 

21 

96362 

22 

88461 

K 

22 

90093 

o 

22 

91665 

22 

93181 

23 

24 

3 

85095 
81730 

78364 
75288 

8, 
£ 

A 

23 

24 

3 

86791 
83489 
80187 
76885 

"1 

vj 

A 

23 
24 
25 
26 

88425 
85184 

8i943 
78702 

fl 

3 

A 

Z3 

24 
25 
2O 

90000 
86817 

83635 
80454 

10 

£ 

A 

27 

73867 

27 

75462 

2l 

77272 

28 

74090 

SPAN, 

SPAN, 

SPAN, 

SPAN, 

56 

56 

56 

56 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

R 

* 

m 

X 

R 

m 

X 

R 

m 

, 

115000 

8 

108303 

14 

104285 

21 

97767 

2 

111428 

9 

105178 

Q 

15 

100892 

22 

94642 

3 

108303 

10 

102053 

X 

16 

•   97767 

§ 

33 

gI5'7 

Q 

4 
5 

105178 
102053 

o 

A 

ii 

12 

98928 
95803, 

N 

^3 

17 
18 

94642 
91S17 

ro 

A 

24 

1  c 

88392 
85267 

VI 

•f 

A 

6 

98928 

«3 

92678 

19 

88392 

26 

82142 

*o 

7 

95803 

20 

85267 

27 

79017 

28 

75892 

XIV 


MOMENTS. 


Mx  =  Jfx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

57 

58 

59 

60 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

* 

R 

m 

X 

* 

m 

X 

R 

m 

i 

116491 

i 

"7931 

i 

119322 

i 

120666 

2 

112983 

2 

114483 

2 

115932 

2 

"7333 

3 
4 

109475 
106405 
'03335 

0 

A 

3 

4 

i  i  1034 
107586 
104569 

0 

A 

3 
4 
S 

112542 
109152 
105762 

o 

/2 

3 

4 

114000 
110666 

o 

fr 

6 

100265 

6 

101552 

6 

102796 

6 

104000 

7 

97195 

7 

98534 

7 

99830 

7 

101083 

8 
9 

109475 
106405 

8 
9 

111034 

107586 

8 
9 

112542 
109152 

8 
9 

114000  . 
110666 

10 

ii 

12 

'3 

103335 
100265 

97195 
94124 

N 

A 

IO 

ii 

12 

104569 
101552 
98534 
955'? 

1 

A 

IO 

ii 

12 
13 

105762 
102796 
99830 
96864 

1 

/3 

IO 

ii 

12 

1  07333 
104000 
101083 
98166 

' 

/3 

14 

15 

105790 
102457 

15 

107241 
103965 

14 
15 

108643 
105423 

H 
15 

IIOOOO 

106833 

IO 

99124 

g 

IO 

100689 

o 

IO 

102203 

Q 

16 

103666 

o 

\l 

96054 
92984 

§ 

A 

17 

18 

97413 
94396 

o1 

A 

17 

98983 
95761 

§ 

/3 

17 
18 

100500 
97333 

§ 

/3 

'9 

89914 

ro 

19 

9'379 

n 

19 

92796 

n 

19 

94166 

" 

20 

86843 

20 

88361 

20 

89830 

20 

91250 

21 

83773 

21 

85345 

21 

86864 

21 

88333 

22 

96054 

22 

97413 

22 

98983 

22 

100500 

23 
24 

§84 
14 

23 

24 

94396 
9  '379 

23 
24 

95761 
92796 

23 
24 

97333 
94166 

25 
26 

43 

83773 
80703 

77633 

| 

A 

25 
26 

27 
28 

8836: 

85345 
82327 

79309 

! 

A 

20 
28" 

89830 
86864 

83897 
80931 

! 

A 

25 
26 
27 
28 

91250 

8S333 
85416 
82500 

I 

A 

29 

74563 

29 

76293 

29 

77965 

29 

79583 

3° 

74500 

30 

76666 

• 

CONCENTRATED  LOAD  SYSTEM. 


XV 


MOMENTS. 


Mx  =  Rx  -  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

61 

62 

63 

64 

feet. 

feet. 

feet. 

feet. 

X 

A> 

m 

X 

R 

in 

X 

A' 

m 

X 

X 

m 

I 

122377 

, 

124032 

I 

125634 

I 

127187 

2 

118688 

2 

120403 

2 

122063 

2 

123671 

3 

115409 

3 

116774 

3 

118492 

3 

120156 

4 

112131 

0 

P* 

4 

H3548 

o 

A 

4 

114920 

o 

A 

4 

116640 

o 

A 

£ 

108852 
'°5573 

| 

110322 
107096 

| 

111746 
108571 

| 

113125 

IIOOOO 

7 

102295 

7 

103870 

7 

105396 

7 

106875 

8 

115409 

8 

116774 

8 

118492 

8 

120156 

9 

112131 

0 

9 

H3548 

g 

9 

114920 

g 

9 

116640 

Q 

10 

ii 

108852 
1  °5573 

n 

A 

10 
ii 

110322 
107096 

M 

ft 

10 
ii 

111746 
108571 

m 
« 

A 

10 
ii 

113125 

IIOOOO 

*o 

A 

12 

102295 

12 

103870 

12 

105396 

12 

106875 

'3 

99426 

'3 

100644 

'3 

IO2222 

'3 

103750 

'4 

111311 

14 

112580 

H 

II3808 

14 

"539° 

15 

108196 

'1 

109516 

15 

IIO792 

15 

112031 

16 

17 
18 

105081 
101966 
98851 

N 

Ps 

16 

17 
18 

106451 
103386 
100322 

N 

Pi 

16 

17 
18 

107777 
104761 
IOI745 

N 

A 

ID 

17 
18 

109061 
106093 
103124 

g 

A 

]9 

95737 

'9 

97257 

ft 

'9 

98729 

19 

100156 

CO 

20 

92622 

20 

94193 

20 

957U 

20 

97188 

21 

B9753 

21 

91128 

21 

92698 

21 

94219 

22 

101966 

23 

103386 

22 

IO476I 

22 

106093 

23 

98851 

23 

100322 

23 

IOI745 

23 

103124 

24 

95737 

24 

97257 

24 

98729 

24 

100156 

25 

92622 

0 

25 

94193 

o 

25 

95713 

25 

97188 

20 

27 
28 

«9753 
86885 
84016 

"1 

3 

f* 

26 

27 
28 

91128 
88365 
85483 

u-l 
vS" 

P* 

27 
28 

86904 

$ 

A 

26 

al 

94219 
91250 
88281 

to 

-ft 

A 

29 

81148 

29 

82660 

2Q 

84126 

29 

85546 

3° 

78279 

30 

79837 

3° 

81348 

30 

,   82812 

31 

75410 

31 

770IS 

3' 

78570 

31 

80078 

32 

75792 

32 

77343 

* 

XVI 


APPENDIX. 


MOMENTS. 


Mx  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

65 

66 

67 

68 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

.r 

K 

m 

• 

* 

m 

jr 

A' 

m 

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128692 

i 

130530 

i 

'  323'  3 

i 

134044 

2 

3 

125231 
121769 

2 

3 

126742 
123333 

3 

128582 
124850 

2 

3 

130367 
126691 

4 

118308 

0 

PZ 

4 

119924 

o 

ft 

4 

121492 

0 

ft 

4 

123014 

o 

A 

0 

7 

114846 
11138; 
108308 

7 

116515 
113106 
109696 

0 

7 

118134 
114776 
111417 

7 

119706 
116398 
1*3089 

8 

121769 

8 

I23333 

8 

124850 

8 

126691 

9 

118308 

Q 

9 

119924 

g 

9 

121492 

o 

9 

123014 

o 

10 
u 

12 

114846 
11138? 
108308 

1 

Pi 

10 
ii 

12 

116515 
113106 
109696 

N 

A 

10 
ii 

12 

118134 
114776 
111417 

1 

A 

10 
ii 

12 

i  19706 
"6398 
113089 

in 

PI 

A 

13 

105230 

13 

106666 

«3 

108059 

'3 

109780 

14 

116923 

14 

118408 

14 

119850 

'4 

121250 

IS 

113615 

115151 

116641 

15 

118088 

16 

i  10307 

16 

111893 

1  6 

"3432 

ID 

114927 

Ii 

107384 
104461 

§ 

ft 

11 

108635 

105756 

§ 

ft 

11 

110223 

107014 

§ 

A 

18 

111765 
108603 

§ 

A 

19 

101538 

ro 

19 

102878 

ft 

19 

104178 

M 

'9 

105441 

ft 

20 

98614 

20 

IOOOOO 

20 

101342 

20 

102647 

21 

95691 

21 

97119 

21 

98506 

21 

99853 

22 

92769 

22 

94241 

22 

95671 

22 

97055 

23 

104461 

23 

105756 

23 

107014 

2,3 

108603 

24 

101538 

24 

102878 

24 

104178 

24 

105441 

25 
26 

98614 
95691 

25 
26 

IOOOOO 

97119 

20 

101342 
98506 

26 

102647 
99853 

28 

89847 

& 

A 

27 
28 

94241 

91363 

& 

A 

27 
28 

95671 
92835 

& 

A 

27 
28 

97055 
94220 

in 

A 

29 

86924 

>O 

2Q 

88484 

O 

29 

90000 

VO 

29 

91471 

* 

3° 
3' 

84232 
81538 

3° 
31 

85705 
82954 

30 

3' 

87163 
84327 

30 

V 

88656 
85863 

32 

78845 

32 

80302 

32 

8'7'5 

32 

83068 

33 

89847 

1 

A 

33 

p* 

1095000 

A 

33 
34 

92835 
90000 

f 

A 

33 
34 

94220 
91471 

IO9500O 

A 

CONCENTRATED  LOAD  SYSTEM. 


MOMENTS. 


=  J?x  —  m. 


UNIVERSITY 


XVII 


Sl'AN, 

SPAN, 

SPAN, 

SPAN, 

69 

70 

7' 

72 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

X 

* 

m 

x 

R 

m 

X 

* 

m 

i 

•35724 

I 

'37357 

i 

139295 

, 

141180 

2 

132101 

2 

'337«5 

2 

'35422 

2 

137361 

3 

128478 

3 

130214 

3 

131901 

3 

'35541 

4 

124855 

o 

p* 

4 

126642 

0 

Pi 

4 

128380 

o 

f* 

4 

130070 

0 

ff 

5 

121231 

5 

123071 

5 

124859 

5 

126600 

6 

117971 

6 

119500 

6 

121338 

6 

123129 

7 

114710 

7 

i  16285 

7 

117816 

7 

119658 

8 

i  28478 

8 

130214 

8 

131901 

8 

'3354' 

9 

124855 

g 

9 

126642 

g 

9 

128380 

g 

9 

130070 

g 

10 

ii 

121231 

117971 

& 

ft 

10 

ii 

123071 
119500 

N 

A 

10 
ii 

124859 
121338 

& 

Pi 

10 
ii 

126600 
123129 

8, 

Pi 

12 

114710 

'"' 

12 

116285 

"" 

12 

117816 

W 

12 

i  19658 

M 

•3 

111449 

«3 

113071 

'3 

114646 

'3 

116187 

'4 

122970 

M 

1  2464  1 

14 

126264 

'4 

127853 

15 

i  19492 

15 

I2I2I2 

15 

122882 

15 

124520 

16 

17 

116375 
113260 

°. 

16 
17 

117784 
II47I2 

g 

16 

17 

119501 
116118 

\ 

p. 

16 

'7 

121187 
"7853 

n 

Pi 

.8 

i  10144 

pi 

18 

111641 

PI 

Pi 

18 

113090 

ro 

18 

114520 

fl 
t*S 

'9 

107028 

r*1 

'9 

108570 

ro 

'9 

110062 

'9 

"1534 

20 

103912 

20 

105500 

20 

107035 

20 

108547 

21 

101158 

21 

102427 



21 

119501 

21 

121187 

22 

113260 

22 

1I47I2 

22 

116118 

22 

"7853 

23 

110144 

23 

111641 

23 

113090 

23 

114520 

24 

107028 

24 

108570 

24 

110062 

24 

'"534 

25 

103912 

25 

105500 

25 

107035 

25 

108547 

26 

101158 

§ 

26 

102427 

o 

26 

104006 

g 

26 

105562 

0 

27 
28 

98405 
95652 

$ 

P4 

28 

99713 
97000 

& 

A 

11 

100978 
98302 

* 

A 

27 
28 

102576 
99589 

& 

ft 

29 

92897 

29 

94284 

VO 

29 

95626 

O 

29 

96951 

O 

30 

90144 

30 

91570 

30 

92949 

30 

94312 

31 

8739° 

88857 

3' 

90274 

3' 

91672 

32 

84637 

32 

33 

86143 

83428 

32 
33 

87598 
84921 

32 

33 

89039 
86395 

33 

95652 

0 

34 
35 

92897 
90144 

f 

Pi 

34 
35 

94284 
91570 

f 

ft 

34 

9 

95626 
92949 
90274 

I 

ft 

34 
35 
36 

96951 
943  '2 
91672 

f 

Pi 

- 

XV111 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


1  — 

SPAN, 

,73 
feet. 

SPAN, 

74 
feet. 

SPAN, 
fe7el 

SPAN, 
76 
feet. 

X 

R 

m 

X 

j? 

m 

X 

R 

;« 

X- 

R 

m 

i 

2 

3 

4 

7 

143013 
139246 

'35479 
131712 
128287 
124863 
121438 

0 

N 

A 

I 

2 

3 

4 

'44797 
141081 

137365 
133649 
129933 
126555 

o 

A 

I 
2 

3 

4 

146533 
142866 
139200 

"35533 
131866 
128200 

o 

A 

I 

2 

3 
4 

1 

148223 
144605 
140986 
137368 
133750 
130131 

o 

A 

8 
9 

10 

u 

12 
13 

141081 
137365 
133649 
129933 
126555 
123176 
119798 

10 

Cl 

A 

8 
9 

10 

ii 

12 
'3 

142866 
139200 

'35533 
131866  . 
128200 
124866 
I2I533 

"i 

w 

A 

8 

9 
10 
ii 

12 
13 

144605 
140986 
137368 
133750 
I3OI3' 
126513 
123223 

»o 
N 

A 

8 
9 

10 

ii 

12 
13 

'35479 
131712 
128287 
124863 
121438 
118013 

A 

'4 
15 

16 

17 
18 

'9 

20 

•29383 
126095 
122807 
119520 
116232 
"2945 

IIOOOO 

N 

(O 

A 

14 

!i 

il 

19 

20 

131216 
127635 

'2439' 
121148 
117904 
114661 
111418 

c* 

n 

A 

'4 
15 
16 

11 

'9 

133000 
129460 
125933 
122733 
"9533 
"6333 

M 
CO 

A 

'4 

'5 
16 

'7 
18 

'9 

134776 
131249 
127762 
124266 
121118 
"7959 

O 

N 

f) 

A 

20 

21 
22 
23 

24 
25 
26 
27 
28 
29 
30 

3' 

32 

129466 

"5933 
122733 

"9533 
"6333 
i'3'33 
109933 
107066 
104200 

101333 
98466 
95600 
93066 

"1 
$ 

\ 

A 

20 

21 

22 
23 
24 
25 
26 

27 
28 
29 

3° 
3' 

131249 
127762 
124266 
121118 
117959 
i  i  4802 
111644 
108486 
105657 
102828 

IOOOOO 

97170 

*si 
3 

A 

21 

22 
23 
24 
25 
2O 

2! 
29 
30 

31 
S2 
33 

122807 
119520 
116232 
112945 

IIOOOO 

107054 
104108 
101164 
98218 
95616 
93012 
90410 
87807 

U"l 

^S" 

A 

21 

22 
23 
24 

26 

S 

29 

3° 
31 
32 
33 

I2439I 
121148 
117904 
114661 
111418 
108513 
105607 
102701 

99797 
96891 

94323 

9'756 
89188 

-i? 

A 

32 
33 
34 

36 
P 

108486 
105657 
102828 

IOOOOO 

97170 

94341 
91841 

f 

Ps 

33 

34 
35 
36 
37 
38 

104200 
101333 
98466 
95600 
93066 
9°533 

tO 

£ 

A 

34 
35 
3° 

37 

98218 
95616 
93012 
90410 

I 

A 

34 

P 

37 

99797 
96891 

94323 
91756 

I 

£ 

A 

. 

CONCENTRATED  LOAD  SYSTEM. 


XIX 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

77 

78 

79 

80 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

• 

X 

* 

m 

X 

* 

in 

X 

* 

m 

I 

149870 

I 

151666 

I 

I534I7 

I 

«55'*S 

2 

146298 

2 

147948 

2 

149746 

2 

151500 

3 

142727 

3 

M4423 

3 

146075 

3 

"47875 

4 

'39155 

o 

p2 

4 

140897 

o 

/2 

4 

142594 

0 

Pi 

4 

144250 

o 

/2 

I 

132013 

I 

"3737" 
'33845 

\ 

139"3 

| 

140812 

'37375 

7 

128442 

7 

130319 

7 

132151 

7 

'33937 

8 

142727 

8 

'44423 

8 

146075 

8 

M7875 

9 

I39I55 

n 

9 

140897 

g 

9 

142594 

o 

9 

144250 

Q 

10 
ii 

"35584 
132013 

I 

ft 

1°. 

n 

I3737I 
"33845 

| 

fl 

10 
ii 

"391  13 
135632  . 

1 

fl 

10 
ii 

140812 
'37375 

& 

A 

12 

128442 

M 

12 

130319 

M 

I  ** 

132151 

|-1 

12 

'33937 

"* 

'3 

124871 

'3 

126793 

'3 

128670 

'3 

130500 

'4 

136429 

14 

138074 

'4 

140000 

"4 

141874 

17 

132987 

"29545 
126104 

g 

Pi 

3 

'7 

134677 
131280 

127882 

M 

f, 

3 

"7 

136328 

132974 
129620 

N 

fl 

15 
16 
'7 

138250 
134624 
"3'3'2 

M 

^3 

18 

122662 

" 

18 

124484 

ro 

18 

126265 

18 

128000 

19 

119546 

'9 

121088 

'9 

140000 

IQ 

141874 

20 

132987 

20 

"34677 

20 

136328 

20 

138250 

21 

129545 

21 

131280 

21 

132974 

21 

134624 

22 

126104 

22 

127882 

22 

129620 

22 

'3'312 

Q 

23 

122662 

23 

124484 

Q 

23 

126265 

g 

23 

128000 

g 

24 

y 

119546 
116429 
"33'2 

1 

VO 

p. 

24 
•>  r 

26 

121088 
118010 
"4933 

! 

ft 

24 
26 

122910 
119556 
116518 

3 

A 

24 
25 
26 

124687 

'21374 
118062 

3 

27 

110195 

27 

111857 

27 

113480 

27 

115062 

28 

107077 

28 

108780 

28 

110442 

28 

112062 

29 

104286 

29 

105702 

29 

107404 

3° 

101494 

29 

124687 

30 

uSoio 

30 

"9556 

30 

"21374 

3' 

i'33'2 

3" 

"4933 

3' 

116518 

31 

118062 

32 

110195 

32 

111857 

32 

113480 

32 

115062 

33 

107077 

108780 

0 

110442 

33 

112062 

0 

34 
35 
36 

104286 
101494 
98701 

S? 

fl 

34 
35 
36 

105702 
102946 
100190 

10 

IT 

ft 

34 

9 

107404 
104366 
101644 

S? 

A 

34 

109062 
106062 
103062 

f 

A 

38 

95909 
93116 

38 

97433 
94677 

P 

98923 
96201 

38 

"00375 
97687 

39 

90650 

39 

91923 

39 

93480 

39 

95000 

40 

90759 

40 

92312 

XX 


APPENDIX. 


MOMENTS. 


Mx  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAR, 

81 

82 

83 

84 

feet. 

feet. 

feet. 

feet. 

JC 

K 

m 

X 

* 

m 

X 

• 

m 

* 

* 

m 

I 

156790 
153209 

I 

2 

158414 
154878 

I 

2 

160180 
156506 

i 

2 

161904 
158273 

3 

149629 

3 

'5I34I 

3 

153012 

3 

154642 

4 

146049 

o 

ft 

4 

147804 

o 

ft 

4 

149518 

o 

p* 

4 

151190 

o 

A 

7 

142469 
139074 
"35679 

7 

144268 

140731 

137378 

3 

7 

146024 
142530 
139036 

1 

7 

M7738 
144285 

140833 

8 

149629 

8 

I$»341 

8 

153012 

S 

154642 

9 

146049 

g 

Q 

147804 

Q 

9 

149518 

O 

9 

151190 

g 

10 

ii 

12 

'3 

142469 
139074 
135679 
132283 

M 

/3 

10 
ii 

I  ** 

'3 

144268 

140731 
137378 
134024 

1 

A 

10 
ii 

12 

'3 

146024 
142530 

139036 

135722 

VO 

Pi 

IO 

ii 
'3 

147738 
.  144285 
140833 
137300 

P? 

ft 

'4 

143702 

'4 

145487 

'4 

147228 

14 

148938 

15 

140122 

g 

15 

I4I951 

g 

15 

'43734 

9 

15 

'45475 

9, 

16 

136542 

g 

ft 

16 

138414 

g 

Pi 

16 

140239 

g 

ft 

16 

142023 

g 

^ 

'7 

132962 

N 

'7 

jj, 

17 

136746 

ro 

i? 

'38570 

fo 

18 

129691 

18 

I3'3'4 

18 

133251 

18 

135118 

'9 

143702 

'9 

145487 

'9 

147228 

'9 

•148938 

20 

140122 

20 

141951 

20 

143734 

20 

'45475 

21 

136542 

21 

138414 

21 

140239 

g 

21 

142023 

o 

22 
23 

24 

132962 
129691 
126418 

ft 

22 
23 

24 

134877 
I3I341 
128109 

I 

P* 

22 
23 
24 

136746 
'33251 
1=9757 

1 

A 

22 
23 
24 

138570 
135118 
131666 

1 

A 

25 

123147 

*O 

2  1 

124877 

25 

126564 

25 

128214 

20 

119876 

26 

121645 

26 

123372 

2D 

125059 

27 

116604 

27 

118413 

28 

113641 

27 

136746 

27 

138570 

28 

'3'34' 

28 

13325' 

28 

135118 

29 

126418 

29 

128109 

29 

129757 

30 

128214 

30 

123147 

30 

124877 

30 

126564 

o 

32 

121903 

g 

3' 

119876 

3' 

121645 

32 

120179 

u-l 

A 

34 

"5594 

oJ 

ft 

32 

116604 

32 

118413 

34 

"3794 

o 

35 

112440 

g 

33 

34 

113041 
110678 

£ 

33 
34 

115182 
112255 

§ 

36 
38 

108010 
102227 

37 

109582 
106726 

9 

107715 
104752 

$ 

A 

9 

109328 
106401 

$ 

37 
3» 
39 

101789 

99135 
96481 

I 

39 

103475 
100548 
97926 

39 

120179 

1 

ft 

38 
39 

125059 
121903 

i 

ft, 

40 

93826 

40 

95304 

M 

4' 

91172 

4> 

92682 

40 

1  332  5  ' 

$ 

40 

135118 

$ 

4' 

'29757 

8 

p7 

4' 

131666 

h 

42 

126564 

N 

42 

128214 

CONCENTRATED  LOAD  SYSTEM. 


XXI 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

»S 

86 

8? 

88 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

j; 

R 

m 

X 

j? 

m 

• 

.c 

R 

m 

i 

163588 

I 

165232 

i 

166839 

i 

168579 

i 

160000 

2 

161685 

2 

163333 

2 

164943 

3 

156412 

3 

I58I39 

3 

159827 

3 

161477 

4 

152824 

o 

A 

4 

'54593 

o 

A 

4 

156321 

o 

A 

4 

158011 

o 

A 

149412 

5 

151046 

5 

152816 

5 

'54545 

6 

146000 

6 

147674 

6 

149310 

6 

'5'079 

7 

142588 

7 

144302 

7 

'45977 

7 

'47613 

8 

156412 

8 

158139 

8 

159827 

8 

161477 

9 

152824 

o 

9 

'54593 

Q 

9 

156321 

o 

9 

158011 

o 

10 

ii 

149412 
146000 

i*~i 

H 

A 

10 

ii 

151046 
147674 

LO 

M 

A 

10 

ii 

152816 
149310 

""i 
n 

A 

10 

ii 

'54545 
151079 

LO 

C) 

A 

12 

142588 

** 

12 

144302 

I  2 

'45977 

M 

1  2 

'47613 

l~l 

13 

'391?? 

'3 

140930 

'3 

142643 

'3 

M43I7 

'4 

150587 

'4 

152383 

'4 

'54'37 

'4 

'5595' 

15 

M7I7S 

g 

'5 

148837 

g 

15 

150632 

o 

15 

152386 

Q 

16 
17 

M3763 
I40351 

PI 

A 

16 
'7 

145464 
142092 

8 

A 

16 
17 

147125 

143792 

8 

A 

16 
'7 

148919 

'45454 

8 

A 

18 

'36939 

rt 

1  8 

138720 

fO 

18 

140458 

ro 

18 

142158 

!•> 

19 

133528 

'9 

'35348 

'9 

137125 

'9 

138863 

20 

I47I75 

20 

148837 

20 

1  50632 

20 

152386 

21 

143763 

21 

145464 

21 

147125 

21 

148919 

22 

I40351 

Q 

22 

142092 

Q 

22 

143792 

O 

22 

'45454 

Q 

23 
24 

136939 

133528 

u-i 

3 

A 

23 
24 

138720 
135348 

V) 

3 

A 

23 
24 

140458 
137125 

1 

A 

23 
24 

142158 
138863 

1O 

3- 

A 

3 

130115 
126704 

25 
26 

131976 
128604 

25 

'33793 
'3°459 

>o 

-y  p 

26 

'35567 
132272 

vO 

27 

127126 

27 

i  28976 

27 

14035' 

27 

142092 



28 

136939 

28 

138720 

28 

140458 

28 

142158 

29 

'33528 

29 

135348 

29 

'37'25 

29 

138863 

3° 

130115 

8 

30 

'3'976 

§ 

30 

'33793 

o 

30 

135567 

Q 

31 

32 

126704 
123586 

LO 

° 

A 

3' 

32 

128604 
125232 

& 

g1 

A 

3' 
32 

130459 
127126 

i? 

A 

3' 

32 

132272 
i  28976 

in 

8" 

A 

33 

120469 

3.3 

122150 

33 

123792 

33 

125680 

34 

"735' 

34 

119068 

34 

120746 

34 

122385 

35 

114233 

35 

115986 

35 

117701 

35 

'  '9373 

36 

1  33528 

a 

36 

135348  ' 

9 

36 

I37'25 

36 

138863 

„ 

37 
38 

130115 
1  26704 

1 

A 

3 

131976 
128604 

1 

A 

3 

'33793 
i30459 

1 

A 

% 

135567 
132272 

1 

A 

39 

127126 

M 

39 

128976 

- 

39 

14035' 

39 

142092 

• 

40 

136939 

8 

40 

138720 

8 

40 

140458 

40 

142158 

41 

133528 

8^ 

A 

4i 

135348 

§1 

A 

4i 

137125 

8 

4' 

138863 

0 

42 

!30"5 

Wl 

42 

131976 

"i 

N 

42 

'33793 

Si 

A 

42 

'35567 

»o 

A 

43 

126704 

43 

128604 

43 

'30459 

»o 

43 

132272 

IT) 

44 

127126 

44 

128976 

xxu 


APPENDIX. 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

.  SPAN, 

SPAN, 

SPAN, 

89 

89 

90 

90 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

* 

Jf 

m 

X 

R 

m 

X 

- 

m 

i 

2 

3 

4 

170280 
166685 
163089 
159662 
156235 

0 

A 

40 

42 
43 
44 

143819 
140561 

137303 
134044 
130786 

2550000 

A 

i 

2 

3 
4 

171943 
168388 
164832 
161277 

157888 

o 

A 

40 
4' 
42 
43 

44 

145610 
142222 
139000 
'35777 
132555 

I 

A 

6 

152808 

o 

154500 

7 

149382 

§ 

7 

151110 

0 

8 
9 

163089 
159662 

45 

143819 

N 

f! 

A 

8 
0 

164832 
161277 

45 

145610 

r^ 

CO 

* 

10 
ii 

156235 
152808 

« 

A 

10 
ii 

157888 
154500 

N 

A 

12 

149382 

I~I 

12 

151110 

*"* 

'3 

'45955 

'3 

147721 

'4 

157527 

'4 

159166 

17 

154100 
150673 
147246 

1 

A 

:i 

'7 

155776 
152388 
149000 

1 

A 

18 

143819 

fO 

18 

145610 

n 

'9 

140561 

'9 

142222 

20 

154100 

20 

155776 

21 

150673 

21 

152388 

22 

147246 

Q 

22 

149000 

Q 

23 

24 

143819 
140561 

1 

A 

23 
24 

145610 
142222 

* 

A 

25 

137303 

\o 

25 

139000 

26 

134044 

2O 

'35777 

27 

130786 

27 

28 

143819 

28 

145610 

29 

140561 

29 

142222 

3° 

137303 

o 

30 

139000 

Q 

3' 
32 

134044 
130786 

1 

A 

3' 

32 

'35777 
132555 

£ 

A 

33 

127527 

M 

33 

129333 

- 

34 

124269 

34 

126110 

35 

I2IOIO 

35 

122888 

36 

140561 

e 

36 

142222 

g 

38 

'37303 
134044 

1 

A 

37 
38 

139000 

'35777 

| 

A 

39 

130786 

39 

132555 

M 

CONCENTRATED  LOAD  SYSTEM. 


XX111 


MOMENTS, 


X  =  J?x  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

91 

9' 

92 

92 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

* 

R 

„ 

X 

ff 

m 

* 

J? 

m 

i 

'7357' 

28 

14736' 

i 

'75l63 

28 

149075 

2 

3 

170054 
166538 

29 

30 

144011 
140660 

. 

2 

3 

171684 
168206 

29 
30 

145760 
142444 

4 

163021 
159505 

0 

ft 

3' 

32 

'37473 
134286 

1 

ft 

4 

164728 
161250 

o 

ft 

3' 
32 

139129 

'35977 

1 

ft 

7 

I56I53 
1  52802 

33 

34 

131100 
127912 

M 

7 

'5777' 
154456 

33 
34 

132825 
129673 

M 

35 

124725 

35 

126521 

8 

166538 

8 

168206 

9 

10 

ii 

12 

163021 
159505 
I56I53 
I  52802 

M 

ft 

36 
39 

144011 
140660 

'37473 
134286 

1 

f» 

9 
10 
ii 

12 

164728 
161250 

'5777' 
154456 

M 

» 

36 

37 
38 
39 

145760 
142444 
139129 
'35977 

I 

ft 

'3 

149450 

'3 

151141 

40 
4' 

14736' 
144011 

, 

40 
4' 

149075 
145760 

. 

'4 

160933 

'4 

162662 

'5 

157417 

n 

42 

140660 

8 

Pi 

15 

159183 

g 

42 

142444 

8 

Pi 

16 

'7 
18 

154065 
IS07I3 
I4736I 

M 

CO 

ft 

43 
44 

137473 
134286  . 

" 

16 

'7 
18 

'55705 
152390 
149075 

1 

S3 

43 
44 

139129 
'35977 

« 

'9 

I44OII 

g 

'9 

145760 

0 

20 

I574I7 

45 
46 

144011 

N 

ft 

20 

I59I83 

45 
46 

149075 
145760 

£ 

ft 

21 

154065 

21 

155705 

22 

I507I3 

o 

22 

152390 

g 

23 

24 
25 

I4736I 
I44OII 
140660 

3 

A 

23 

24 

149075 
145760 
142444 

1 

A 

26 

'37473 

2O 

139129 

27 

134286 

27 

'35977 

XXIV 


APPENDIX. 


MOMENTS. 


Mx  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

93 

93 

94 

94 

feet. 

feet. 

feet. 

feet. 

X 

- 

m 

X 

A1 

m 

X 

A' 

m 

X 

A' 

m 

, 

I7688I 

28 

150752 

I 

178563 

28 

152392 

2 

173279 

29 

147472 

2 

175000 

29 

149147 

3 

4 

I 

7 

169838 
166397 
1  62956 
I595I6 
156075 

o 

A 

3' 
32 
33 
34 

144192 
140913 
137634 

I3I397 

$ 

A 

3 
4 

7 

168031 
164627 
161223 
157819 

0 

A 

3' 
32 
33 
34 

145902 
142658 

'39413 
136168 

'33083 

I 

A 

35 

128279 

35 

130000 

3° 

125161 

3" 

126913 

8 

169838 

8 

171436 

9 

166397 

s 

9 

168031 

o 

10 

ii 

12 

13 

162957 
I595I6 
156075 
I52795 

N 

A 

t 

39 
40 

144192 
140913 
137634 
I345'6 

I 

A 

10 

ii 

12 

'3 

164627 
161223 
157819 
I544I4 

1 

A 

37 
38 
39 
40 

145902 
142658 

136168 

1 

A 

14 

164354 

41 

147472 

'4 

166010 

4' 

149147 

. 

II 

17 

160913 

157472 
I5403I 

N 

A 

42 
43 
44 

144192 
140913 
137634 

to 

A 

15 
16 
17 

162605 
159201 
155796 

| 

A 

42 
43 
44 

145902 
142658 
I394I3 

1 

A 

18 

150752 

ro 

18 

152392 

'9 

M7472 

19 

149147 

45 

150752 

8 

45 

152392 

8 

46 

147472 

Jo 

A 

46 

149147 

to 

A 

20 

160913 

47 

144192 

w 

20 

162605 

47 

145902 

fO 

21 

157472 

21 

159201 

22 

I5403I 

o 

22 

155796 

£ 

23 

24 

150752 
147472 

1 

A 

23 

24 

152392 
149147 

:? 

A 

25 

I44I92 

\o 

25 

145902 

26 

140913 

26 

142658 

27 

137634 

27 

I394I3 

- 

CONCENTRATED    LOAD    SYSTEM. 


MOMENTS. 


M,  =  Rx  —  m. 


UNIVERSITY 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

95 

95 

96 

96 

feet. 

feet. 

feet. 

feet. 

X 

R 

;« 

X 

R 

m 

X 

K 

m 

X 

R 

m 

I 

180211 

4' 

150788 

I 

181822 

4' 

152552 

2 

3 

4 

176684 

'73157 
169631 
166263 

0 

f* 

42 
43 
44 

147578 
144367 
141157 

1 

ft 

2 

3 

4 

178333 
174843 
I7I354 
167864 

0 

A 

42 
43 
44 

149219 
146042 
142865 

I 

ft 

6 

162894 

6 

'6453' 

7 

159526 

45 
46 

150788 

§ 

7 

161197 

45 
46 

155885 
152552 

§ 

8 

'73'57 

47 
48 

147578 
144367 

VO 
t^ 

o 
CO 

pa 

8 

'74843 

47 
48 

149219 
146042 

S 

ft 

9 

169631 

g 

9 

I7I354 

o 

10 

ii 

166263 
162894 

1 

ft 

10 
ii 

167864 
'6453' 

r» 

ft 

12 

159526 

'-t 

I  ** 

161197 

*" 

'3 

156157 

'3 

157864 

'4 

'67631 

'4 

169374 

\l 

17 

164262 
160894 

'57525 

1 

ft 

'7 

165884 
162551 
159218 

n 

ft 

18 

I54I57 

R 

18 

155885 

to 

'9 

150788 

'9 

152552 

20 

164262 

20 

165884 

21 

160894 

21 

162551 

22 

157525 

n 

22 

159218 

o 

23 
24 

I54I57 
150788 

| 

A 

23 
24 

155885 
152552 

* 

A 

147578 

VO 

25 

149219 

VO 

26 

'44367 

26 

T46o42 

27 

141157 

27 

142865 

28 

I54I57 

28 

155885 

29 

150788 

29 

152552 

30 

147578 

3° 

149219 

3' 

144367 

8 

3' 

146042 

8 

32 
33 

141157 
137948 

I 

h 

32 
33 

142865 
139689 

f 

ft 

34 

134738 

34 

136512 

35 

131686 

35 

'33335 

36 

i  28634 

36 

'3°3'4 

37 

147578 

37 

149219 

38 
39 

144367 
141157 

1 

ft 

38 
39 

146042 
142865 

1 

ft 

40 

137948 

40 

139689 

XXVI 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

97 

97 

98 

98 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

X 

- 

„ 

X 

R 

m 

X 

K 

„ 

i 

2 

3 

4 

183525 
179948 
176494 

0 

A 

4! 

42 
43 
44 

150978 
147679 
'44535 
141391 

2550000 

A 

i 

2 

3 
4 

185193 
181653 
178112 
174693 

o 

41 
42 

43 
44 

155968 
152703 
149438 
146173 

H 

A 

i 

169587 
166134 

| 

171275 
167857 

7 

162835 

a 

157576 
154278 

8 

7 

164438 

45 
46 

159234 
155968 

0 

47 

150978 

Si 

A 

47 

& 

A 

8 

176494 

48 

147679 

£T 

8 

178112 

48 

149438 

M 

9 

173041 

g 

49 

I4453S 

9 

174693 

Q 

49 

146173 

10 

ii 

169587 
166134 

N 

A 

10 

ii 

171275 
167857 

1 

A- 

12 

162835 

1-1 

12 

164438 

W 

13 

159536 

'3 

161173 

14 

171082 

'4 

172754 

II 

167628 
164175 

8 

15 

169335 
165917 

8 

17 

160875 

N 

pi 

17 

162500 

w 

/3 

18 

157576 

ro 

18 

159234 

to 

19 

154278 

19 

155968 

20 

167628 

20 

169335 

21 

164175 

21 

165917 

22 

160875 

Q 

22 

162500 

g 

23 

24 

157576 
i  54278 

1 

A 

24 

159234 

155968 

I 

A 

25 

150978 

VO 

25 

152703 

>o 

26 

147679 

26 

149438 

27 

144535 

27 

146173 

28 

157576 

28 

159234 

29 

154278 

29 

155968 

30 

150978 

3° 

152703 

3! 

147679 

8 

3i 

149438 

g 

32 

144535 

o\ 

A 

32 

146173 

<s 

A 

33 
34 

141391 
138246 

» 

33 

34 

143060 
139948 

~ 

# 

35 

135102 

136836 

36 

132958 

36 

133724 

39 

150978 
147679 
'44535 

1 

A 

i 
39 

152703 
149438 
146173 

1 

A 

40 

141391 

40 

143060 

CONCENTRATED    LOAD  SYSTEM. 


XXV11 


MOMENTS. 


M,  —  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

99 

99 

IOO 

too 

feet. 

feet. 

feet. 

feet. 

X 

V? 

m 

.*• 

R 

m 

.* 

R 

m 

JT 

R 

m 

I 

186828 

4' 

157625 

I 

188430 

4' 

159250 

2 

3 
4 

183323 
179818 

176313 

o 

A 

42 
43 
44 

'54393 
151160 
147928 

"•> 

M 

A 

2 

3 
4 

184960 
181490 
178020 

o 

A 

42 
43 
44 

156050 
152850 
149650 

U"> 

w 

A 

5 

172924 

5 

'7455° 

6 

169545 

b 

171200 

7 

166161 

41 

160858 

7 

167850 

45 

162600 

40 

157625 

Q 

46 

159250 

5 

8 
9 

179818 
176313 

47 
48 

49 

'54393 
151160 
147928 

"1 
fN. 

W 

ro 

A 

8 
9 

181490 
178020 

47 
48 

49 

156050 
152850 
149650 

r-N, 

N 

to 

/» 

10 
ii 

172929 
169545 

»^> 

N 

A 

5° 

144696 

10 

ii 

'7455° 
171200 

»>•> 

N 

A 

12 

166161 

M 

12 

167850 

§ 

13 

162777 

'3 

164500 

5° 

178020 

i 

/,0 

H 

174393 

'4 

176000 

15 

171000 

o 

15 

172650 

g 

l6 

'7 

167625 
164241 

A 

16 

17 

169300 
165950 

A 

18 

160858 

to 

18 

162600 

«n 

19 

157625 

'9 

159250 

20 

171009 

20 

172650 

21 

167625 

21 

169300 

22 

164241 

o 

22 

165950 

§ 

23 
24 

160858 

157625 

•<t- 

A 

23 
24 

162600 
159250 

»/i 
3 

A 

25 

'54393 

VO 

25 

156050 

20 

151160 

26 

152850 

27 

147928 

27 

165950 

28 

160858 

28 

162600 

29 

157625 

29 

159250 

3° 

'54393 

3° 

156050 

0 

3' 
32 
33 

151160 
147928 
144696 

vn 

81 

A 

3' 
32 

33 

152850 
149650 
146450 

>0 

£ 

A 

34 

141615 

34 

'4325° 

35 

'38534 

35 

140200 

36 

'35454 

36 

13715° 

37 

'54393 

37 

156050 

38 
39 

151160 
147928 

I 

A 

3« 
39 

152850 
149650 

1 

A 

40 

144696 

40 

146450 

XXV111 


APPENDIX. 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

"°3 

103 

105 

105 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

jr 

R 

m 

X 

- 

m 

X 

A' 

m 

I 

•7 

3 

193281 
189796 
186310 

42 

43 

164368 
161115 
157963 

I 

Pi 

i 

2 
1 

196438 
193019 
189600 

4' 
42 
43 

167619 
164429 
161234 

1 

4 

182941 

o 

/2 

44 

154611 

10 

4 

186180 

o 

fl 

44 

158048 

io 

5 

179572 

45 

151504 

182761 

45 

154858 

6 

176203 

6 

"79457 

7 

172834 

7 

176152 

46 

164368 

Q 

46 

167619 

Q 

8 
9 

186310 
182941 

47 
48 

49 

161115 

157963 
154611 

PI 

P> 

8 
9 

189600 
186180 

47 
48 
49 

164429 
161234 

158048 

N 

ft 

10 

ii 

"79572 
176203 

& 

A 

10 
ii 

182761 
"79457 

| 

h 

12 
'3 

172834 
169466 

50 
5' 

182941 
179572 

Pa 

12 
13 

176152 
172848 

So 

170952 

§ 

A 

S2 

176203 

€ 

Q 

"4 

181067 

H 

184400 

* 

17 

18 

177669 
174271 

170873 
167620 

M 

CO 

* 

15 

16 

'7 
18 

180953 
177619 
173286 
170952 

I 

fl 

5" 

52 
53 

182761 

179457 
176152 

00 

/.o 

19 

164368 

'9 

167619 

20 

177669 

20 

180953 

21 

174271 

21 

177619 

22 

170873 

Q 

22 

173286 

„ 

24 

167620 
164368 

& 

PA 

23 

24 

170952 
167619 

& 

ft 

3 

161115 

157963 

V 

25 
26 

164429 
161234 

<0 

27 

154611 

27 

158048 

28 

167620 

28 

170952 

29 

164368 

29 

167619 

30 

161115 

164429 

3' 

"57963 

0 

V 

161234 

8 

32 

154611 

Pi 

32 

158048 

10 

Ps 

33 

i5I5°4 

6 

33 

154858 

g1 

34 

148398 

34 

151668 

35 

145290 

148621 

36 

142183 

36 

"45574 

3 

39 

161115 

157963 
154611 

1 

Po 

39 

164429 
161234 
158048 

| 

ft 

40 

151504 

40 

154858 

CONCENTRATED  LOAD  SYSTEM. 


XXIX 


MOMENTS. 


x  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

108 

1  08 

IIO 

IIO 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

X 

R 

m 

X 

* 

m 

X 

R 

m 

I 

200953 

4' 

172684 

I 

203827 

4' 

176017 

2 

197629 

42 

169443 

8 

2 

200563 

42 

172726 

8 

3 

4 

194305 
190981 

o 

f* 

43 
44 

166202 
162962 

1 

A 

3 
4 

197300 
194036 

o 

* 

43 

44 

169545 
166362 

to 

A 

187657 

45 

159861 

5 

190772 

45 

163181 

6 

184333 

6 

187509 

7 

181009 

7 

184245 

46 

172684 

o 

46 

176017 

p, 

8 
9 

194305 
190981 

47 
48 
49 

169443 
166202 
162962 

N 

A 

8 
9 

197300 
194036 

47 
48 

49 

172726 

169545 
166362 

£ 

N 
CO 

A 

10 

II 

187657 
184333 

1 

A 

10 
ii 

190772 
187509 

I 

Pi 

12 

181009 

w 

g 

12 

184245 

*" 

o 

'3 

177685 

5° 
51 

175925 
172684 

8, 

A 

'3 

180981 

50 
S' 

179308 
176017 

& 

A 

'4 

'5 

189333 
185981 

* 



'4 
'S 

192581 
189181 

* 

16 

\l 

'9 

182629 

179277 
175925 
172684 

! 

A 

52 
53 
54 

184333 
181009 
177685 

I 

Ao 

16 

'7 
18 

'9 

185890 
182599 
179308 
176017 

1 

f, 

53 
54 

187509 
184245 
180981 

00 

/.o 

20 

185981 

20 

189181 

21 

22 

182629 

179277 

21 

22 

185890 
182599 

55 

203827 

8 

A. 

23 
24 

175925 
172684 

1 

A 

23 
24 

179308 
176017 

I 

A 

0 

25 

'69443 

vO 

25 

172726 

VQ 

26 

166202 

26 

169545 

27 

162962 

27 

166362 

28 

175925 

28 

179308 

29 

172684 

29 

176017 

3° 

169443 

172726 

31 

166202 

O 

31 

169545 

g 

33 

162962 
159861 

i? 

A 

32 

33 

166362 
163181 

<? 

A 

34 

156759 

34 

160000 

35 

153657 

156953 

36 

150556 

36 

153908 

37 

169443 

g 

37 

172726 

39 

166202 
162962 

| 

A 

38 
39 

169545 
166362 

| 

A 

40 

159861 

40 

163181 

XXX 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

"3 

"3 

115 

|  |  C 

feet. 

feet. 

feet. 

feet. 

,*• 

* 

m 

* 

R 

m 

X 

R 

m 

X 

* 

m 

i 

2 

208159 
204876 

4' 
42 

180957 
'77753 

3 

I 

2 

210991 
207765 

37 

180956 
177809 

. 

3 
4 

201592 
198415 

0 

A 

43 
44 
45 

17455° 
171346 
168144 

N 

A 

3 

4 
5 

204539 
201313 
198086 

o 

A 

39 

40 

174660 
171512 
168364 

M 

A 

7 

192061 
188884 

6 

7 

194965 
191843 

46 

180957 

o 

42 

180956 

Q* 

8 
9 

10 

ii 

201592 
19841? 

195238 
192061 

| 

A 

47 
48 
49 

'77753 
'7455° 
171346 

N 
CO 

P. 

8 

9 
10 
n 

2°4539 

198086 
194965 

VO 
N 

A 

43 
44 
45 

177809 
174660 
171512 

n 

A 

12 

'3 

188884 
185707 

5° 
5' 

184160 
180957 

§ 

&n 

12 
13 

191843 
188721 

46 
47 

184207 
180956 

8 

52 

'77753 

t- 

48 

177809 

^ 

53 

17455° 

§ 

49 

174660 

N 

'4 

'97397 

'4 

200468 

5° 

171512 

15 

194088 

8 

15 

197217 

0 

17 
18 
'9 

190778 
187470 
184160 
180957 

N 

A 

54 

185707 

| 

I 

17 
18 
'9 

193964 
190712 
187460 
184207 

1 

A 

5' 
52 
53 

184207 
180956 
177809 

1 

A 

54 

174660 

§ 

CO 
21 
22 

194088 
190778 
187470 

55 
56 

208159 
204876 

| 

20 

21 

22 

197217 
193964 
190712 

O 

23 

184160 

g 

57 

201592 

>s 

23 

187460 

55 

200468 

8 

/I0 

24 

180957 

•? 

/< 

24 

184207 

>n 

pt 

25 

'77753 

VO 

25 

180956 

v? 

27 
28 

171346 
168144 

27 
28 

174660 
171512 

56 

i 

207765 
204539 

| 

AI 

5° 

201313 

N 

29 

180957 

29 

184207 

* 

30 

'77753 

3° 

180956 

3r 

174550 

O 

3! 

177809 

32 

171346 

8 

A 

32 

174660 

33 

168144 

g\ 

T< 

171512 

?? 

5 

34 

165046 

-I 

168364 

M 

35 

161949 

35 

165216 

36 

158852 

36 

162172 

37 

'77753 

38 

174550 

8 

39 

171346 

8 

ft 

4° 

168144 

CONCENTRATED  LOAD  SYSTEM. 


XXXI 


MOMENTS. 


Mx  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

1  20 

1  20 

125 

125 

feet. 

feet. 

feet. 

feet. 

X 

A' 

m 

X 

* 

m 

X 

A> 

m 

JT 

R 

m 

\ 

2 

3 

218058 
214866 
211675 

38 
39 
40 

185883 
182766 
179650 

1 

A 

I 
2 

225040 
221880 
218720 

40 

4' 
42 

187424 
184432 
181440 

\ 

A 

4 

208483 

0 

A 

4' 

176533 

- 

4 

215560 

o 

0 

43 

I78448 

S.' 

5 

205291 

5 

212400 

p* 

6 

202200 

6 

209336 

7 

I99IO8 

42 
43 
44 

189000 
185883 
182766 

1 

2>7 

* 

206272 
203208 

44 

45 
46 

190416 
187424 
184432 

1 

A 

8 

211675 

45 

179650 

!/•! 

47 

181440 

io 

9 

208483 

46 

176533 

8 

48 

178448 

10 

205291 

. 

9 

215024 

g 

A 

ii 

202200 

M 

12 

'3 

I99IO8 
196016 

47 
48 

189000 
185883 

3 

49 

5° 

190416 
187424 

g 

49 

182766 

10 

ft 

10 

212400 

51 

184432 

& 

A 

14 

207800 

5° 

179650 
176533 

£ 

ii 

12 

209336 
206272 

a 

M 

A 

S2 
53 

181440 

178448 

N 

15 
16 

204583 
201466 

0 

13 

203208 

17 

198350 

b1 

P^ 

52 

189000 

S4 

190416 

Q 

'9 

195233 
I92II6 

CO 

53 

S4 

185883 
182766 

§> 

A 

14 

15 

215024 
211840 

55 
S6 

187424 
184432 

IO 

A 

20 

iSgOOO 

SS 

179650 

o" 

ID 

208752 

£ 

S7 

181440 

% 

56 

'76533 

17 

205664 

§ 

18 

202576 

N 

/"a 

21 

22 
23 

24 

201466 
198350 

195233 
I92Il6 

, 

P 

201466 
198350 

I 

Ao 

'9 

20 

21 

199488 
196400 
193408 

58 

205664 
202576 
199488 

VO 

Ao 

25 

iSgOOO 
*  TCrXS-> 

MT" 

J  4 

10 

«°5OOJ 

22 

205664 

27 
28 

179650 

g 

205291 

2O22OO 

1 

23 
24 

202576 
199488 
196400 
193408 

| 

61 
62 

206272 
203208 

N 

A. 

29 

192116 

>s 

27 

190416 

V? 

3° 

189000 

28 

187424 

31 

185883 

2Q 

184432 

32 

33 

182766 
179650 

A 

3° 

181440 

63 

215024 

§ 

A- 

34 

'76533 

6 

£r 

37 

I734i6 
170389 
167372 

31 

32 

193408 
190416 
-  187424 

" 

34 

184432 

8 

181440 

S 

A 

^6 

178448 

8' 

37 

175456 

^O 

172464 

39 

'69472 

xxxn 


APPENDIX. 


MOMENTS. 


Mx  =  Rx  —  m. 


SPAN, 
130 
feet. 

SPAN, 
130 

feet. 

SPAN, 

/3S 

feet. 

SPAN, 

/35 

feet. 

X 

^ 

m 

jr 

y? 

m 

X 

R 

m 

.r 

R 

m 

i 

2 

3 

4 

1 

8 

231946 
228815 
225684 

222553 
219422 
216383 

2I3345 
210306 

0 

N 

M 

A 

40 
41 
42 

43 
44 

194783 
191813 
188844 
185968 
183090 

I 

A 

I 

2 

3 

4 

1 

238429 

235414 
232400 
229385 
226370 

223354 
220339 
217324 

o 

A 
A 

40 
41 

42 
43 
44 
45 

202042 
199094 
196146 
193287 
190428 
187568 

8 

A 

45 
46 

47 
48 

49 

194783 
191813 
188844 
185968 
183090 

*o 
in 

N 

A 

46 

47 
48 

49 
5° 

199094 
196146 
193287 
190428 
187568 

10 
10 

N 

A 

9 

10 

ii 

222152 
218998 
215936 

A 

9 

10 

ii 

12 

«3 

228498 
226072 
223035 
219998 
216961 

pi 

SO 
51 

52 
53 
54 

194783 
191813 
188844 
185968 
183090 

10 
r-. 

N 

ro 

/a 

12 
13 

213345 
210306 

tn 
N 

M 

A 

Si 

52 
53 
54 
55 

199094 
196146 
193287 
190428 
187568 

r-, 

N 
C*) 

A 

14 
15 
16 

11 

'9 

20 

21 

228498 
226072 
223035 
219998 
216961 
213924 
210887 
207939 

N 
CO 

A 

14 
15 

16 
17 
18 
19 

20 
21 

222152 
218998 
215936 
212875 
209814 
206752 
203690 
200721 

n 

A 

P 

$ 

J94783 
191813 
188844 
185968 

tv. 

1 

A 

56 

i 
59 

60 
61 
62 
63 

199094 
196146 
193287 
190428 

«-n 

& 

ST 

A 

§ 
61 

209814 
206752 
203690 

f 

*o 

Ao 

A. 

22 
23 
24 
25 
26 

27 
28 
29 

3° 

219998 
216961 
213924 
210887 
207939 
204991 
202042 
199094 
196146 

u-i 

£ 

A 

213924 
210887 
207939 
204991 

iO 

<O 
to 

/.o 

22 
23 
24 

25 
26 
27 
28 
29 

3° 

212875 
209814 
206752 
203690 
200721 
197752 
194783 
191813 
188844 

VO 

£ 

A 

62 

210306 

1 

64 

a 

% 

226072 

223035 
219998 
216961 
213924 

fN. 

r>. 

A. 

3' 
32 
33 
34 
35 
36 
37 
38 
39 

207939 
204991 
202042 
199094 
196146 
193287 
190428 
187568 
184708 

m 

$ 

A 

63 
64 

65 

222152 
218998 
215936 

r^ 
r^. 

Ai 

31 
32 
33 
34 
35 
36 

i 

39 

200721 
197752 
194783 
191813 
188844 
185968 
183090 
180214 
177326 

U-l 

<T 

A 

CONCENTRATED  LOAD  SYSTEM. 


MOMENTS. 


M,  =  Rx  — 


XXXlll 


SPAN, 

Sl'AN, 

SPAN, 

SPAN, 

140 

140 

'45 

'45 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

* 

* 

m 

X 

R 

m 

JC 

* 

m 

I 

244792 

4' 

206285 

I 

251131 

41 

213391 

2 

241800 

42 

203356 

8 

2 

248158 

42 

210481 

8 

3 

238807 

43 

200514 

8 

ft 

3 

245186 

43 

207653 

8 

ft 

4 
5 

232821 

o 

f* 

44 
45 

197671 
194827 

- 

4 

242213 
239241 

0 

f. 

44 

204825 
201998 

S 

6 

229914 

6 

23635' 

7 

227007 

7 

233461 

8 

224100 

46 

206285 

8 

230571 

46 

213391 

47 

203356 

Q 

47 

210481 

X 

9 

236084 

48 
49 

200514 
197671 

& 

p. 

9 

242578 

48 
49 

207653 

204825 

3 

P7 

10 

233070 

8 

SO 

194827 

10 

239585 

8 

SO 

201998 

ii 

230056 

8 

Pi 

ii 

236674 

M 

ft 

12 

227042 

M 

12 

233764 

13 

224028 

5' 

206285 

13 

230853 

51 

213391 

t 

S2 

203356 

A 

52 

210481 

0 

14 

15 

236084 
233070 

53 
54 
SS 

200514 
197671 
194827 

M 

P. 

'4 

15 

242578 
239585 

53 
54 

SS 

207653 
204825 
201998 

1 

C) 

ft 

16 

230056 

o 

10 

236674 

56 

199170 

'7 

227042 

8 

p. 

17 

233764 

8 

18 

224028 

?i 

56 

206285 

18 

230853 

5 

ft 

'9 

20 
21 

221014 
218000 
213070 

9 

§ 

203356 
200514 
197671 
194827 

4075000 

ft 

19 

20 
21 
22 

227943 
225032 

222122 
2I92II 

to 

9 

CQ 

OO 

210481 
207653 

204825 
201998 

4075000 

ft 

„„ 

227042 



— 

23 

224028 

61 

218000 

8 

23 

230853 

61 

225032 

24 
25 

221014 
218000 

g 

62 
63 

215070 
212142 

i? 

fa 

24 

2  ^ 

227943 
225032 

62 
63 

222122 
2I92II 

§ 

fo 

26 

215070 

¥ 

ft 

"j 

26 

222122 

§ 

64 

216301 

VD 

27 
28 
29 
30 

209213 
206285 
203356 

64 

a 

233070 
230056 
227042 

. 

•h,. 

27 
28 
29 
30 
3' 

216301 

2I339I 
210481 
207653 

9 

Pi, 

6S 

213391 

66 

67 

233764 

68 

r-. 

68 

227043 

31 

32 
33 
34 

215070 
212142 
209213 
206285 

69 

70 

218000 
215070 

fs. 

32 

33 
34 

2I92II 
216301 

2I3391 

69 

70 
71 

72 

225032 
222122 
2I92U 
216301 

1 

fa 

9 

203356 
•  200514 

£ 

h 

35 
36 

210481 

207653 

& 

P-, 

73 

2I339I 

37 

197671 

37 

204825 

S1 

38 

194827 

38 

201998 

39 

191985 

39 

199170 

40 

189142 

40 

!9°343 

XXXIV 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

'5° 

150 

'55 

J55 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

.AT 

* 

m 

* 

- 

m 

X 

A' 

m 

I 

2 

257446 
254493 

42 

43 

217533 
214720 

8 

i 

2 

263741 
260806 

43 

44 

221403 
218681 

g 

3 

251540 

44 

211906 

8 

Ai 

3 

257870 

4S 

215958 

8 

A 

4 

248586 
245633 

o 

A 

45 
46 

209093 
206280 

2 

4 

254935 
252000 

o 

A 

46 

47 

213236 

210515 

- 

6 

242760 

6 

249141 

7 

239866 

7 

246283 

8 

237013 

47 

217533 

8 

243425 

48 

221403 

48 

214720 

Q 

49 

218681 

o 

49 

211906 

8 

Pi 

50 

215958 

8 

AT 

9 

249040 

SO 

209093 

m 

9 

255470 

51 

213236 

v^l 

10 

246066 

g 

Si 

206280 

N 

10 

252515 

8 

S2 

210515 

M 

ii 

243173 

8 

/2 

n 

249638 

8 

A 

53 

207793 

12 

240280 

« 

12 

246761 

M 

'  13 

237386 

52 

217533 

'3 

243883 

53 

214720 

X 

p% 

S4 

218681 

S4 

211906 

in 

55 

215958 

| 

14 

249040 

ss 

209093 

N 

'4 

255470 

56 

213236 

IT) 

A 

15 

246066 

S6 

206280 

15 

252515 

57 

210515 

Cl 

16 

243173 

16 

249638 

58 

207793 

17 

240280 

8 

«z 

246761 

8 

18 

'9 

20 

21 
22 

237386 

234493 
231600 
228786 
225973 

to 

A 

9 

61 

217533 
214720 
211906 
209093 
206280 

4075000 

A 

18 

'9 

20 

21 
22 

243883 
241006 
238128 

232528 

& 

A 

g 

61 
62 

218681 
215958 
213236 
210515 

O 

A 

6a 

203466 

63 

207793 

23 

237386 

23 

243883 

24 

3 

27 
28 

29 

234493 
231600 
228786 

225973 
223160 
220346 

iO 

A 

63 
64 

65 
66 
67 

225973 
223160 
220346 

217533 
214720 

I 

/,„ 

24 
25 
26 

27 

28 

29 

241006 
238128 
235328 
232528 
229727 
226926 

I 

A 

64 

65 
66 
67 
68 

229727 
226926 
224126 
221403 
218681 

1 

,,. 

3° 

217533 

3° 

224126 

31 

214720 

68 
6q 

234493 
231600 

3i 
32 

221403 
218681 

69 
70 

238128 
235328 

32 
33 
34 

9 
9 

39 

225973 
.   223160 
220346 

217533 
214720 
211906 
209093 
206280 

1 

A 

70 
71 
72 
73 
74 
75 

228786 

225973 
223160 
220346 

217533 
214720 

7170000 

A. 

7' 
72 

73 
74 
75 
76 

77 
78 

232528 
229727 
226926 
224126 
221403 
218681 
215958 
213236 

r-*. 

* 

33 
34 
35 
36 

9 

39 

229727 
226926 
224126 
221403 
218681 
215958 
213236 

1095000 

A 

40 

203466 

40 

210515 

4[ 

200733 

4' 

207793 

42 

205070 

CONCENTRATED    LOAD    SYSTEM. 


XXXV 


MOMENTS. 


x  —  Rx  —  m. 


SPAN, 
160 
feet. 

SPAN, 
160 
feet. 

SPAN, 
160 
feet. 

SPAN, 
165 
feet. 

X 

- 

m 

^ 

* 

m 

^ 

* 

wz 

- 

* 

m 

I 

269725 

39 

219829  • 

R 

75 

227967 

i 

275624 

2 

3 
4 

266881 
264037 
261193 
258350 

o 

A 

40 
42 

217116 
214486 
211849 

in 

If 

A 

7° 
77 
78 
79 

225254 
222541 
219829 
217116 

| 

A. 

2 

3 
4 

272793 
269963 
267133 
264303 

o 

A 

8 

255506 
252662 
249818 

43 
44 

227967 
225254 

8 

261545 
258787 
256030 

45 
46 

222541 
219829 

\ 

A. 

So 

227967 

1 

A* 

9 

261880 

47 

217116 

>- 

00 

Q 

26818! 

10 

258942 

§ 

48 

214486 

10 

265333 

g 

ii 

256079 

§ 

A 

ii 

262484 

g 

12 

253'97 

2 

12 

259636 

M 

13 

250354 

49 

5° 

225254 
2221:41 

13 

14 

256787 
253938 

219829 

8 

14 

261880 

52 

217116 

u-l 

A 

15 

258942 

214486 

N 

15 

265333 

16 

256079 

54 

211849 

16 

262484 

17 

253197 

g 

'7 

259636 

18 

250354 

2 

18 

256787 

8 

'9 

20 
21 

247491 
244628 
241840 

& 

P 

222541 
219829 
217116 

| 

'9 

20 

21 

25393s 
251089 

248313 

fO 

/3 

22 

239053 

58 

214486 

r^ 

A 

22 

245537 

23 

236255 

59 

211849 

f) 

23 

242761 

60 

209212 

24 

247491 

24 

253938 

25 
26 

244628 
241840 

61 

62 

219829 
217116 

§ 

25 
26 

251089 
248313 

27 
28 

29 

239053 
236255 
2  "?34^7 

! 

A 

£ 

64 

214486 
211849 

° 

A 

11 
29 

245537 
242761 
239986 

Tj- 

A 

3° 

.V 

237211 

3' 
32 

227967 
225254 

$ 

233467 
230680 

§ 

31 

32 

234507 
231804 

67 

§1 

10 

33 

236255 

68 

225254 

8, 

33 

242761 

34 

233467 

o 

•(4 

239986 

Q 

35 
36 

230680 
227967 
225254 

f 

A 

69 

70 

244628 
241840 

p 

35 
36 

37 

237211 
234W 
231804 

f 

A 

38 

222541 

72 

236255 

II 

38 

229101 

73 

233467 

74 

230680 

XXXVI 


APPENDIX. 


MOMENTS. 


Mx  =  J?x  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

-65 

165 

170 

170 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

* 

m 

X 

R 

m 

X 

R 

m 

39 
40 

41 
42 

226397 
223696 
221072 
218447 

in 
$ 

ft 

76 

H 

231804 
229101 
226397 
223696 

t-* 

Pn 

I 

2 

3 
4 

281535 
278717 
275900 
273082 

40 

42 
43 

230235 
227611 
224987 
222364 

1095000 

ft 

43 

215823 

80 

221072 

5 

270264 

A 

6 

267517 

44 

45 
46 

47 

231804 
229101 
226397 
223696 

| 

ft 

Si 

82 
83 

231804 
229101 
226397 

i- 

M 

CO 

PK 

8 

264770 
262023 

44 

45 
46 

47 
48 

238317 
235624 
232929 
230235 
227611 

1 

A 

9 

274188 

48 

221072 

10 

271353 

0 

ii 

268687 

a 

^ 

49 

5° 

231804 
229101 

12 

"3 

14 

265823 
263059 
260294 

- 

49 
50 
Si 

238317 
235624 
232929 

§ 

5' 

52 

226397 
223696 

! 

P7 

S3 

230235 
227611 

M 

53 

221072 

Cl 

15 

271353 

S4 

224987 

54 

218447 

16 

268687 

17 

265823 

18 

263059 

§ 

55 

235624 

55 

229101 

'9 

260294 

8 

ft 

S6 

232929 

0 

56 

8 

226397 
223696 
221072 

1 

A 

20 

21 
22 

257529 
254764 
252000 

8 

S9 

230235 
227611 
224987 

m 

A 

£ 

218447 
215823 

t-5 

23 

249235 

60 

222364 

24 

260294 

61 

232929 

61 
62 

226397 
223696 

g 

25 
26 

257529 
254764 

62- 

230235 
227611 

§ 

A 

63 
64 
65 

221072 
218447 

215823 

1 

P-, 

27 
28 
29 

252000 

249235 
246470 

! 

ft 

64 
65 

224987 
222364 

1 

3° 

243705 

66 
67 

237211 
234507 

j 

31 
32 
33 

238317 
235624 

66 

67 
68 

243705 
241010 

238317 

Sn 

/.o 

68 

fro 

235624 

69 

229101 

34 

246470 

70 

72 
73 

248313 
245537 
242761 
239986 

r^ 

35 
36 

39 

243705 
241010 

238317 
235624 
232929 

m 

ft 

70 
7' 

72 
73 
74 

254764 
252000 

249235 
246470 

243705 

| 

,., 

74 

237211 

r~ 

75 

241010 

75 

234507 

78 

238317 

CONCENTRATED  LOAD  SYSTEM. 


XXXV11 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

170 

^75 

'75 

'75 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

* 

m 

X 

R 

m 

X 

R 

m 

77 
78 
79 

235624 
232930 
230235 

I 

A- 

i 

2 

3 

287451 
284645 
281840 

42 
43 

231508 
228890 

in 

8 

ft 

77 
78 
79 

242114 
239428 
236742 

\ 

A. 

So 

227611 

"• 

4 

5 

279034 
276228 

o 

A 

80 

234125 

**• 

b 

27349  ' 

81 
82 

238317 
235624 

g 

8 

270754 
268017 

44 

4S 

244800 
242114 

g 

81 

82 

244800 
242114 

83 
84 

232929 

230235 
227611 

M 

00 

* 

46 

47 
48 

239428 
236742 
234125 

1 

A 

83 
84 
85 

239428 
236742 
234125 

u-t 

Jj 

A* 

9 

280194 

10 

277370 

Q 

86 

231508 

ii 

274616 

g 

87 

228890 

12 
13 
14 

271862 
269108 
266353 

fl 

f» 

49 

So 
Si 

244800 
242114 
239428 

§ 

88 

226273 

52 

236742 

"-) 

53 

234125 

IS 

277370 

16 

274616 

19 

2O 
21 
22 
23 

271862 
269108 
266353 
263600 
260914 
258228 
255542 

ri 

pi 

54 
55 
56 

I 

244800 
242114 
239428 
236742 
234125 
231508 
228890 

"I 

ft 

- 

24 

252857 

61 
62 

63 

64 

239428 
236742 
234125 
231508 

£ 

A 

25 
26 

27 

263600 
260914 

258228 

28 

255542 

§ 

6S 

228890 

29 

252857 

& 

P4 

31 

32 

33 

247485 
244800 
242114 

66 

67 
68 

250171 
247485 
244800 

1 

60 

34 

252857 

70 

239428 

250171 

39 
40 

247485 
244800 
242114 
239428 
236742 
234125 

f 

Ps 

72 
73 
74 

9 

258228 
255542 
252857 
250171 

247485 
244800 

£ 

A. 

XXXV111 


APPENDIX. 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

1  80 

180 

180 

185 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

R 

m 

X 

* 

m 

X 

R 

m 

i 

2 

3 
4 

I 

293372 
290577 
287783 
284988 
282194 
279466 

0 

A 

42 
43 
44 

240610 
238000 
235391 
232777 

f 

* 

80 

Si 

82 

240610 
238000 
235391 

| 

A. 

i 

3 
4 

i 

299037 
296318 
293600 
290881 
288162 
285443 

o 

A 

I 

276738 
274010 

45 
46 

248444 
245833 

8 

83 
84 

245833 
243221 

8 

282724 
280005 

47 

243221 

5 

A 

8c 

240610 

X 

48 

240610 

& 

86 

238000 

Si 

A. 

9 
10 
ii 

286200 
283388 
280644 

8 

49 

'238000 

87 
88 
89 

235391 
232777 
230166 

00 

9 
10 
ii 

292204 
289404 
286669 

8 

A 

12 
13 
14 

277900 

275!55 
272410 

' 

ft 

50 

S2 
53 
54 
55 

248444 

245833 
243221 
240610 
238000 
235391 

1 

A 
A 

90 

227621 

For  all  values  of 
x  below  x  —  67, 
a  uniformly  dis- 
tributed load  of 
3000  Ibs.  per  ft. 
will  give  greater 
moments  than 
this  table. 

12 
'3 
H 

283934 
281120 
278464 

" 

15 

16 

17 
18 

"9 

20 
21 
22 

23 

283388 
280644 
277900 

275'55 
272410 
269665 
266988 
264310 
261633 

| 

* 

15 
ID 

? 

2O 
21 
22 

»3 

289404 
286669 
283934 
281120 
278464 
275729 

270388 
267717 

1 

A 

56 
P 
S 

245833 
243221 
240610 
238000 
235391 

I 

24 

258955 

24 

265047 

61 

245833 

25 
26 
27 
28 

29 

3° 

269665 
266988 
264310 
261633 

258955 
256277 

1 

A 

62 

f3 
64 

67 

243221 
240610 
238000 
235391 
232777 
230166 

1 

A 

25 
26 
27 
28 
29 
30 

275729 
273058 
270388 
267717 
265047 
262377 

T 

A 

31 

253655 

*O 

31 

259770 

33 
34 

251055 
248444 
245833 

68 
69 

70 

251055 
248444 

245833 

1 

Ao 

32 

33 
34 

257165 
254560 
25'955 

35 

256277 

71 

72 

243221 
240610 

35 

262377 

3° 

39 

40 

251055 
248444 
245833 
243221 

f 

Pi 

73 
74 
75 

258955 
256277 

253655 

. 

37 
38 
39 
40 

257165 
254560 

251955 
249350 

if 

A 

?6 

251055 

77 

248444 

78 

245833 

""" 

79 

243221 

CONCENTRATED    LOAD  SYSTEM. 


XXXIX 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

185 

185 

190 

190 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

* 

R 

m 

X 

S 

m 

X 

R 

m 

4' 

246810 

80 

246810 

I 

304657 

41 

252932 

42 
43 

44 

244269 
241729 
239188 

\r\ 

° 

A 

8l 

82 
83 
84 

244269 
241729 
239188 
236647 

1 

fa 

2 

3 
4 

301947 
299236 
296526 
293815 

0 

A 

42 
43 
44 

'45 

250396 
247859 
245322 
242785 

I 

h 

6 

291167 

46 

254560 

25'955 

85 

246810 

8 

288520 
285872 

46 

258069 

47 

249350 

§ 

86 

244269 

47 

255469 

g 

48 

246810 

8 

Pf> 

87 

241729 

a 

48 

252932 

8 

ft 

49 

244269 

8\ 

oo 

oo 

239188 

8 

9 

298145 

49 

250396 

& 

5° 

241729 

89 

236647 

^j- 

fa 

10 

295418 

o 

5° 

247859 

5r 

239188 

90 

234106 

oo 

II 

292692 

§ 

. 

9' 

231566 

12 

289965 

M 

?' 

S2 

249350 

92 
93 

229024 
230284 

'3 
14 

287238 
284511 

51 

52 

258069 
255469 

53 

246810 

o 

53 

252932 

o 

54 

9 

57 

244269 
241729 
239188 
236647 

»o 

Cl 

A 

For  all  values  of 
x  below  x=  57, 
a  uniformly  dis- 
tributed load  of 
3000  Ibs.  per  ft. 
will  give  greater 
moments  than 
this  table. 

\l 

17 
18 

'9 

20 
21 
22 

295418 
292692 
289965 
287238 
284511 
281785 
279122 
276459 

<•! 

A 

54 

9 

57 

250396 

247859 
245322 
242785 

1/1 

w 

Pi 

58 

246810 
244269 

241729 

1 

58 

252932 
250396 
247859 

, 

61 
62 

239188 
236647 

£ 

23 
24 

273795 
271132 

61 
62 

245322 
242785 

p» 

/. 

03 

240315 

67 
68 

246810 
244269 
241729 
239188 
236647 
234106 

10 

A 

3 

27 
28 

29 

30 

281785 
279122 
276459 
273795 
271132 
268469 
265869 

. 

A 

64 
| 

250396 
247»59 
245322 
242785 
240315 

1 

A 

69 

70 

254560 
25I9S5 

1 

32 

33 
34 

260669 
258069 

69 

70 

260669 
258069 

J 

24935° 

Ao 

71 

255469 

10 

A» 

72 
73 

246810 
244269 

«o 

9 

268469 
265869 

8 

72 
73 

252932 
250396 

10 

74 
75 
76 

262377 
259770 
257165 

. 

39 
40 

263269 
260669 
258069 
255469 

f 

,, 

74 
75 
76 

268469 
265869 
263269 

1 

A. 

77 

254560 

R 

At 

77 

260669 

M 

78 

R 

78 

258069 

79 

24935° 

xl 


APPENDIX. 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

190 

195 

'95 

195 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

R 

m 

, 

* 

m 

X 

* 

* 

79 
80 
81 
82 
§3 

255469 
252932 
250396 
247859 
245322 

1 

/.i 

I 

2 

3 
4 

310297 

307595 
304892 
302189 
299487 

0 

A 

42 
43 
44 
45 

259056 
256522 
253989 

25M55 
248922 

1095000 

A 

8 

81 
82 
83 

261589 
259056 
256522 
253989 

25'455 

| 

A. 

84 

242785 

6 

296846 

84 

248922 

8S 

240315 

7 

294205 

8S 

246450 

8 

291564 

46 

264184 

47 

261  589 

o 

86 
87 

250396 
247859 

Q 

303846 

48 
49 

259056 
256522 

§ 

A 

86 

87 

256522 
253989 

88 

245322 

10 

301128 

So 

253989 

- 

88 

25M55 

89 

242785 

o 

ii 

298471 

g 

5' 

251455 

89 

248922 

90 
9' 

240315 
237841 

1 

A. 

12 
13 

295815 

% 

A 



90 

246450 
243978 

§ 

92 

235368 

oo 

'4 

290502 

S2 

261589 

92 

241506 

&> 

/.* 

93 

94 
95 

232894 
230420 
227946 

'5 

287845 

53 
54 
55 
56 

259056 
256522 
253989 
25M55 

2550000 

A 

93 
94 

9 

239035 
236564 

234153 

00 

16 

298471 

For  all  values  of 

17 
18 

295815 
293158 

57 

248922 

97 

yS 

229333 
226923 

x  below  x  —  50, 

19 

290502 

Q 

a  uniformly  dis- 
tributed load  of 
3000  Ibs.  per  ft. 
will  give  greater 
moments    than 
this  table. 

20 

21 
22 
23 
24 

287805 
285189 
282532 
279876 
277219 

N 
ro 

A 

58 
59 
60 
61 
62 

259056 
256522 

253989 
251455 
248922 

3275000 

A 

For  all  values  of 
x  below  x  =  45, 
a  uniformly  dis- 
tributed load  of 
3000  Ibs.  per  ft. 

25 
26 

287845 
285189 

a 

259056 
256522 

0 

this  table. 

27 
28 

282532 
279876 

i 

253989 
25I45S 

1 

A 

29 

30 

277219 
274563 

S 

A 

6? 

68 

248922 
246450 

* 

3' 

271969 

MJ 

269374 

33 
34 

266779 
264184 

69 

70 

266779 
264184 

g 

71 

26l  <$Q 

§ 

/I0 

72 

259056 

vo' 

35 
36 

274563 
271969 

g 

73 

256522 

57 

269374 

O 

38 
39 
40 

266779 
264184 
261589 

ff 

5 

74 
75 
76 

274563 
271964 
269374 

1 

fu 

77 

266779 

~ 

7« 

264184 

CONCENTRATED  LOAD  SYSTEM. 


Xli 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

200 

200 

200 

210 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

X 

* 

m 

jr 

K 

m 

X 

* 

m 

I 

3  '5955 

41 

265170 

7Q 

267700 

I 

327090 

2 

313260 

42 

262640 

8 

80 

265170 

2 

324466 

3 
4 

310565 
307870 

o 

A 

43 

44 

260110 

257580 
255050 

f 

A 

00  00  OO 
U)  10  « 

262640 
260110 

257580 

1 

A, 

3 

4 

321842 
319219 
3  '6595 

o 

A 

6 

302540 

84 

25505° 

6 

3'39?i 

7 

299905 

85 

252580 

7 

3'  '347 

8 

297270 

46 

270290 

8 

308723 

47 

267700 

0 

48 

265170 

0 

86 

262640 

9 

309560 

4P 

262640 

8 

6 

87 

260110 

Q 

321028 

10 

306850 

260110 

M 

88 

257580 

10 

3l8333 

ii 

304200 

o 

5« 

257580 

89 

255050 

II 

315694 

g 

12 

3°  '55° 

8 

* 

90 

252580 

12 

3  '3056 

X 

t. 

13 

298900 

n 

J^Z 

Qi 

250110 

13 

310418 

11 

296250 
293600 
291010 

S2 
53 
S4 

267700 
265170 
262640 

8 

92 
93 
94 

247640 
245170 
242700 

N 

OO 

A* 

'4 

'5 

16 

307780 
305142 
302561 

55 
S6 

260110 

257580 

f, 

A 

9 

240290 
237880 

17 

19 

2O 

3OI550 
298900 
296250 
293600 

8 

57 

255050 

99 

IOO 

235470 
233060 
230650 
228300 

'7 
18 

'9 

20 

3  '3056 
310418 
307780 
305142 

58 

265170 

21 
22 
23 
24 

25 

291010 

288420 
285750 
283240 
280650 

Cl 

A 

§ 

61 
62 
63 

262640 
260110 

257580 

25505° 
252580 

1 

; 

For  all  values  of 
x  below  jr=4i, 
a  uniformly  dis- 
tributed toad  of 

21 
22 
23 

24 
25 

302561 
299980 
297400 
294818 

292237 

M 

A 

3000  Ibs.  per  ft. 

will  give  greater 

26 

291010 
288420 

64 

262640 
260110 

moments  than 
this  table. 

26 

27 

302561 
299980 

29 
30 

3' 
32 

285750 
283240 
280650 
278060 

275470 

3 

A 

67 
68 
69 

257580 
255050 
252580 
250110 

1 

A 

28 
29 

3° 
31 

32 

297400 
294818 
292237 
289713 
287190 

! 

A 

33 

272880 

284666 

34 

270290 

70 

270290 

„ 

34 

35 

282142 
279618 

9 

280650 
278060 

72 

73 
74 

265170 
262640 
260110 

in 

Ao 

36 

289713 

37 

275470 

O 

37 

287190 

8 

272880 

0 

284666 

& 

A 

39 

40 

270290 
267700 

1 

A 

75 
76 

278060 
275470 

8 

A. 

39 
40 

282142 
279618 

8' 

77 

272880 

r^ 

78 

270290 

• 

xlii 


APPENDIX. 


MOMENTS. 


=  Rx  — 


m. 


SPAN, 

210 

feet. 

SPAN, 

2IO 

feet. 

SPAN, 
220 
feet. 

SPAI> 
220 
feet 

r, 

X 

* 

m 

* 

R 

m 

* 

- 

m 

* 

g 

m 

41 
42 
43 
44 

45 
46 

277152 
274684 
272218 
269751 
267284 
264818 

u 

§ 

A 

i 

8 
82 
8l 

284666 
282142 
279618 
277152 
274684 
272218 
269751 

!->. 

Pn 

; 

i 

337977 
335363 
33275o 
33°I36 

327522 

324963 
322404 

o 

A 

4 
4 
4 
44 
4 
46 

288808 
286344 
283881 
281418 
278954 
276544 

h 
° 

A 

K 

0 

47 

279618 

85 

3  '0845 

47 

2QI27I 

48 
49 
50 

277152 
274684 
272218 

1 

A 

8? 

259884 

c 
10 

332217 
72Qt;oo 

48 
49 

288808 
286344 

g 

5' 

52 

269751 
267284 

88 
8q 

269751 
267284 

ii 

12 

13 

327017 
324445 

T2I572 

ct 

A 

5° 
5' 

52 

281418 
278954 

1 

A 

90 

264818 

!<: 

3'930o 

j 

276544 

54 

274684 

0 

92 

259884 

3 

310720 

-86  4 

55 
56 

272218 
269751 
267284 
264818 

Lf 

N 

A 

94 
95 
96 

97 

257417 
254951 
252542 
250132 
247723 

N 

CO 

A. 

16 

'7 
18 
TO 

327017 

324445 
321872 

1 

283881 
281418 
278954 
276544 

M 

A 

CQ 

27/168/1 

ya 
00 

2453'3 
242904 

20 

316726 

jj 

A 

& 
61 

272218 
269751 

§ 

IOO 

240551 

22 
23 

3'4'54 
311581 
309008 

M 

ro 

60 

283881 

62 

63 
64 

267284 
264818 
262351 

PI 

A 

101 
102 

250132 
247723 

g 

24 
25 

306436 
303862 

61 
62 

63 
64 

281418 
278954 
276544 

274  1  "1C 

A 

'03 

245313 

^? 

PI$ 

ro 

65 
66 

272218 

104 

I05 

242904 

24055' 

I 

26 
27 

311581 

66 

269317 

67 
68 
69 
70 

267284 
264818 
262351 
259884 

1 

A 

ror  all  values  of 
x  below  x  =  33, 
uniformly  dis- 
ributed  load  of 

29 

3° 
31 
32 

309008 
306436 
303862 

3°'344 
298826 
296308 

! 

A 

69 
70 

278954 
276544 
274135 
271726 

1 

A 

will  give  greater 

34 

1C 

293790 

72 

277152 

g 

his  table. 

^COO.-.Q 

73 
74 
75 

274684 
272218 

267284 

to 

« 

36 

g 

39 
40 

298826 
296308 
293790 
291271 

j-> 

$ 

A 

73 
74 
75 
76 

286344 
283881 
281418 

278954 

•ft 

'IO 



CONCENTRATED  LOAD  SYSTEM. 


xliii 


MOMENTS. 


M,  =  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

220 

230 

230 

230 

feet. 

feet. 

feet. 

feet. 

t 

K 

m 

X 

R 

m 

X 

R 

m 

X 

A' 

m 

77 

296308 

I 

348960 

4' 

300495 

78 

305416 

78 

293790 

2 

346356 

42 

298033 

I9 

302956 

79 

291271 

3 

3437S2 

43 

295573 

o 

80 

300495 

So 
81 

288808 
286344 

4 

34H47 
338543 

0 

P* 

44 
4S 

293112 
290651 

f 

A 

81 
82 

298033 
295573 

g 

82 
83 

283881 
281418 

\ 

ft, 

7 

33599' 
333440 

46 

47 

288243 
285834 

84 

293112 
290651 

| 

fa 

84 

278954 

8 

330886 

85 

288243 

1^ 

85 

276544 

86 

285834 

86 

87 
88 
89 

274135 
271726 
269317 
266909 

9 
10 
n 

343268 
340651 
338086 

48 
49 
50 
51 

300495 
298033 

295573 
293112 

1 

ft 

67 
88 

89 

283425 
281017 
278608 

12 

335521 

g 

A 

S2 

290651 

2* 

«3 

332955 

« 

S3 

288243 

90 

288243 

90 

276544 

H 

330390 

9' 

285834 

9' 

274135 

'S 

327825 

92 

283425 

92 
93 
94 

P 
97 
98 

99 

100 
IOI 

271726 
269317 
266909 

264553 
262200 
259844 
257490 
255136 
252781 
248072 

10 

00 

p™ 

54 
55 
56 
57 
58 
59 

298033 

295573 
293112 
290651 
288243 
285834 

I 

A 

93 
94 
95 
96 

97 
98 
99 

100 
IOI 
102 

103 
104 

281017 
278608 
276251 
273894 
271538 
269182 
266826 
264520 
262216 
259912 
257608 

N 

OO 

* 

16 

17 
18 

'9 

20 

21 

22 

23 
24 
2S 

338086 
335521 
332955 
330390 
327825 

325312 
322800 
320286 

317773 
315260 

1 

A 

60 
61 
62 

295573 
293112 
290651 
288243 

, 

A 

102 

259844 

0 

61 

28^814 

N" 

IO4 
105 

257490 

255'36 
252781 

1 

A3 

26 

27 

325312 
322800 

a 

283425 
281017 

n 

3 

264520 
262216 

§ 

fa 

28 
29 

320286 
3'7773 

67 

2  06  I 

107 

108 

259912 
257608 

$ 

106 
107 
108 

262200 

259844 
257490 

1 

/>« 

30 
3r 

32 

315260 
312800 
310338 

S 

A 

68 
69 
70 

288243 
285834 

1 

A 

109 

266826 

109 

I  10 

252781 

o 

33 

34 

307»77 
305416 

7i 

28IOI7 

no 
III 

264520 
262216 

§ 

For  all  values  of 
x  below  .r  =  23, 
a  uniformly  dis- 
tributed load  of 
3000  Ibs.  per  ft. 
will  give  greater 
moments  than 

P 

302956 
300495 

A 

112 

"3 
"4 
"5 

259912 
257608 
255303 
253051 

Below  x  =  6,  a 
uniform  load  of 
3000  Ibs.  per  ft. 

| 

72 
73 
74 
75 
76 
77 

300495 
298033 

295573 
293II2 
290651 
288243 

! 

„. 

P 

39 
40 

3  '0338 
307877 
305416 
302956 

f 

this  table. 

gives   greater 

moments  than 

this  table. 

xliv 


APPENDIX. 


MOMENTS. 


Mx  =  Rx  -  m. 


SPAN, 
240 
feet. 

SPAN, 
240 
feet. 

SPAN, 
240 
feet. 

1  - 

SPAN 
250 
feet. 

X 

A' 

m 

X 

A' 

m 

X 

A> 

m 

X 

A' 

lit 

I 

2 

3 
4 

8 

359579 
357033 
354487 
35!94i 
349395 
346900 

344404 
341908 

0 

/ 

41 

42 

43 
44 
45 
46 
47 
48 

3"758 
309350 
306941 

304532 
302125 
299766 
297408 
295050 

f 

t 

80 

81 

82 

83 
84 

85 
86 

87 
88 

3H758 
309350 
306941 

304532 
302125 
299766 
297408 
295050 
292691 

r*, 
t^ 

Pi 

e 

8 

370260 
367720 
365180 
362640 
360100 
3576o8 
355'66 
352624 

o 

P* 

9 

10 

ii 

354350 
35!79i 
349232 

49 
50 
Si 

309350 
306941 

304532 

1 

89 

90 

9i 

290332 

287975 
285616 

c 

10 

ii 

365072 
362520 

'3 
14 
'5 

340675 
344116 

34I558 
339000 

" 

f» 

52 
53 
54 

302125 
299766 
297408 

1 

?6 

92 
93 

94 

295050 
292691 
290332 

12 

13 
14 

I"! 

3575" 
355008 

352504 

1  ^oooo 

N 

P* 

QC 

.(. 

16 

55 

306941 

96 

285616 

0 

347544 

17 
18 

'9 
20 

21 
22 

346675 
344116 

341558 
339000 

336491 
333982 

M 
f> 

ft 

S6 

I 

£ 
61 

304532 
302125 
299766 
297408 
295050 
292691 

10 
IO 
N 

Pi 

97 
98 

99 

100 
IOI 

1  02 
10; 

203258 
280900 
278541 
276232 
273925 
271616 
269308 

LO 

Tt 
N 
00 

ft, 

17 
18 

'9 

20 

21 
22 

357512 
355008 
352504 
350000 

347544 
345088 

8 
8 

tt 

»J 

33'475 

23 

-3426^2 

ro 

24 
25 
26 

320900 
326458 
324000 

62 

63 
.64 

6r 

302125 
299766 
297408 

10 

P« 

104 

I0( 

106 

278541 
276232 

24 
25 
26 

340176 

337720 
335264 

rr 

N 

;l 

333982 

33'475 

67 

292691 
290332 

fO 

107 
108 
109 

269308 
267000 

27 
28 

345088 

3426T2 

30 

3r 
32 
33 
34 
35 
36 

326458 
324000 

32I54I 
319082 
316625 
314166 

3"758 

IO 

<3 

A 

68 
69 

70 
7i 
72 
73 

299766 
297408 
295050 
292691 
290332 
287975 

1 

f-*. 

O 

^t- 

A 

IIO 

in 

112 

«3 

14 
15 
16 

17 
IS 

264741 
262482 
260225 
257966 
255/08 
253500 
251291 
249082 
246875 

to 

-^- 

£ 

/I3 

29 
30 
31 

32 
33 
34 
35 
36 

340176 
337720 
335264 
332808 
330352 
327896 
325440 
323032 

10 

X 

P* 

244666 

H 
39 
40 

321541 
319082 
316625 
314166 

10 

§• 

Pi 

74 
75 
?6 

% 

79 

306941 

304532 
302125 
299766 
297408 
295050 

10 

«, 

Plo 

20 

242509 

\.  uniform  load 
of  3000  Ibs.  per 
ft.  gives  greater 
moments  than 
this  table. 

38 
39 
40 

332808 
330352 
327896 
325440 

uo 

° 

Ps 

CONCENTRATED    LOAD    SYSTEM. 


xlv 


MOMENTS. 


T*  =  Rx  -  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

250 

250 

250 

260 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

A' 

m 

X 

R 

m 

X 

R 

m 

41 

42 
43 
44 

323032 
320624 
318216 
315808 

So 
Si 
82 
83 

323032 
320624 
318216 
315808 

121 
122 

123 
I24 

262968 
260752 
258536 
256320 

0770000 

#«4 

I 

2 

3 
4 

380857 

378369 
375»8o 

373392 

o 

45 

3  '3400 

84 

3  '3400 

"25 

254152 

5 

370903 

FI 

46 
47 
48 

311040 
308680 
306320 

85 
86 

87 

31  1040 
308680 
306320- 

| 

A. 

Tor  all  values  of 

I 

368415 
365926 

88 

303960 

*• 

x  below  _r  =  120, 

49 
5° 
51 

320624 
318216 
315808 

. 

89 
90 

92 

301600 
299288 
296976 
294664 

tributed  load  of 
2700  Ibs.  per  ft. 
will  give  greater 
moments  than 

9 
10 
ii 

375892 
373345 
370845 

52 

3I34°° 

§ 

6 

12 

368345 

0 

53 

311040 

« 

13 

365845 

w 

f* 

54 

308680 

93 

303960 

H 

363345 

w 

94 

301600 

15 

360845 

95 

299288 

16 

358391 

55 

318216 
315808 

96 

97 

296976 
294664 

57 

313400 

8 

90 

292352 

g 

17 

368345 

S& 

i 

61 

311040 
308680 
306320 
303960 

1 

ft 

99 

IOO 
101 
IO2 

103 

290040 
287776 
285512 
283248 
280984 

N 

oo 

fa 

18 

'9 
20 

21 
22 

365845 
363345 
360845 
358391 
355937 

1 

Pi 

104 

278720 
277456 
274192 

23 
24 

20 

353484 
351030 
348576 
346169 

62 
o"5 

313400 
311040 
308680 

a 

306320 
303960 
301600 

N 

r'l 

P* 

107 

108 

283248 
280984 

77 

355937 

68 

299288 

tog 
no 

278720 
277456 

29 

353484 
351030 

69 
70 
7i 
72 
73 
74 

308680 
306320 
303960 
301600 
299288 
296976 

4075000 

A 

112 

"3 

114 

116 
117 
n8 

274192 
271928 
269664 
267400 
265184 
262968 
260752 
258536 

9445000 

fti 

30 

31 

32 

33 
34 
35 
36 
37 

348576 
346169 
34376i 
341353 
338945 

334176 

L/1 

3 

A 

I  IQ 

75 

315808 

120 

.  254'52 

76 

3  '3400 

O 

77 

311040 

O 

Ao 

78 

308680 

o 

79 

306320 

1 

xlvi 


APPENDIX. 


MOMENTS. 


Mx  =  Jfx  —  m. 


SPAN, 

SPAN, 

SPAN, 

\ 
SPAN, 

260 

260 

260 

270 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

X 

R 

m 

X 

R 

m 

X 

R 

* 

38 
39 

40 

341353 
338945 
336538 
334176 

75 

JQ 

327091 
324730 
322369 
320007 

I 

Ao 

116 

»7 
118 
119 

274530 
272353 
270176 
268000 

1 

A3 

I 

2 

3 
4 

391292 

388807 
386322 

42 

331814 

g 

7Q 

3'7645 

VO 

1  20 

265822 

c\ 

38135' 

O 

P, 

43 
44 

329453 
327091 

? 

A 

oO 

315284 

121 

263646 

7 

3789H 
376470 

45 

324730 

§ 

374029 

46 
47 
48 

322369 
320007 

3  '7645 

Si 

82 

33lgi4 

329453 
327091 

122 
I23 

124 

272353 
270176 
268000 

9 

386532 

84 
85 

86 

87 
88 
89 

00 

324730 
322369 
320007 

3^645 
315284 
312922 
310607 

I 

* 

125 
126 
127 
128 
129 
130 

265822 
263646 
261468 
259291 
257"5 
254984 

| 

Pu 

10 

II 

12 
'3 
14 
15 

16 

384036 
381584 
379'32 
376681 
374228 
371777 

PI 

A 

49 
50 
5i 
52 
53 

33"8i4 
329453 
327091 

32473° 
322369 

| 

A 

54 

320007 

308291 

J3  i 

55 

3  '7645 

92 

305976 

For  all  values  ol 

x  below  x  ~  105 

56 

I 
61 

327091 
324730 
322369 
320007 

3^645 
315284 

10 

A 

93 

94 

9 

315284 
312922 
310607 
308291 
305976 
303661 

a  uniformly  dis- 
tributed load  of 
2700  Ibs.  per  ft 
will  give  greater 
moments    than 
this  table. 

18 

«9 

20 

21 
22 
23 

24 

376681 
374228 
371777 
369325 
366874 
364421 
361969 

H 

A 

99 

301345 

O 

25 

359518 

62 

32473° 

IOO 
101 

299076 
296807 

«* 

OO 

A. 

2O 

357tio 

63 

322369 

294537 

64 

67 
68 

320007 
317645 
3  '5284 
312922 
310607 

N 

A 

103 

104 

I05 
106 

107 

292269 
290000 
287776 

285553 
283330 

27 
28 

29 

3° 
3' 

366874 
364421 
361969 
3595i8 
357110 

A 

32 

354703 

O 

69 

320007 

108 

292269 

33 
34 

352295 
349888 

9 

70 

317645 

O 

109 

290000 

3S 

347480 

7' 

31  ^284 

§ 

no 

287776 

o 

36 

72 
73 

312922 
310607 

o^ 

Pi 

III 

112 

285553 
283330 

"T 

As 

37 

342755 

74 

308291 

"3 

281107 

114 

278883 

"5 

276707 

CONCENTRATED    LOAD  SYSTEM. 


xlvii 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPAN, 

270 

270 

270 

280 

feet. 

feet. 

feet. 

feet. 

X 

* 

m 

* 

R 

m 

- 

X 

R 

m 

X 

* 

m 

38 

352295 

77 

333347 

118 

281444 

i 

401839 

39 

349888 

78 

331028 

o 

119 

279258 

o 

2 

399357 

40 

347480 

79 

328711 

8 

P\o 

j  120 

277118 

8 

3 

396875 

41 

345118 

Q 

80 

326392 

"-> 

121 

274977 

j£ 

13 

4 

394392 

Q 

42 

342755 

O 

A 

81 

324074 

10 

122 

272836 

5 

5 

391910 

f» 

43 

340391 

S 

Pi 

123 

270695 

6 

389471 

44 

338029 

7 

387032 

45 

335665 

82 

340391 

8 

384592 

46 
47 

333347 
33  IQ28 

83 
84 

338029 
335665 

124 
'25 

279258 
277118 

85 

333347 

126 

274977 

9 

397100 

86 

331028 

I27 

272836 

10 

3946o6 

48 
49 

345"8 
342755 

87 
88 

328711 
326392 

I 

A. 

128 
129 

270695 
268555 

| 

n 

12 

392156 
389706 

8 

A 

50 

34039' 

O 

89 

324074 

E" 

'3° 

266458 

r^ 

fu 

'3 

387257 

N 

P2 

51 

338029 

8 

j, 

90 

321800 

131 

264362 

o 

14 

384806 

*" 

S2 

335665 

8 

P6 

319525 

132 

262266 

'5 

382357 

53 

333347 

w 

92 

317251 

260169 

16 

37995° 

54 

331028 

93 

3'4977 

'34 

258073 

55 

328711 

94 

312703 

'35 

255977 

17 

389706 

56 

% 

§ 

61 

338029 
335665 
333347 
331028 
328711 
326392 

1 

» 

9 

97 
98 

99 

IOO 

321800 
319525 
3I725« 
3  '4977 
312703 
310428 

For  all  values  of 
x  below  x  =  74, 
a  uniformly  dis- 
tributed load  of 
2700  Ibs.  per  ft. 
will  give  greater 
moments  than 

18 
'9 

20 
21 
22 
23 

24 

387257 
384806 

382357 
379950 
377542 
375'35 
372727 

r-i 

A 

62 

324074 

IOI 

308155 

«* 

/  12 

this  table. 

25 

370321 

IO2 

305880 

CO 

20 

367956 

103 

303607 

27 

365593 

63 

333347 

104 

301332 

64 

331028 

IO5 

299102 

a 

328711 
326392 

1 

r» 

106 

296873 

28 
29 

375'35 
372727 

67 

fr 

3° 

370321 

68 

321800 

107 

305880 

367956 

g 

69 

3'9525 

108 

303607 

32 

365593 

§1 

A 

109 

301332 

33 

363228 

Tj- 

IIO 

299102 

34 

360863 

70 
7i 

328711 
326392 

in 

112 

296873 
294643 

* 

Pn 

35 
36 

358500 

72 
73 
74 

8 

324074 
321800 

319525 
3^7251 
3'4977 

r^ 
* 

P9 

"3 
"4 
"5 
116 

"7 

292414 
290184 
288000 
285814 
283629 

35377' 
351406 

xlviii 


APPENDIX. 


MOMENTS, 


=  Rx  —  m. 


SPAN, 
280 

SPAN, 
280 

SPAN, 
280 

SPAN, 

feet. 

feet. 

feet. 

fr* 

feet. 

X 

K 

m 

X 

Jt 

« 

X 

* 

m 

X 

* 

m 

39 
40 

42 
43 
44 
45 
46 

47 
48 
49 

360863 
358500 
356135 
353771 
351406 

348043 
346678  . 

344356 
342035 

339713 
337393 

j? 

PI 

77 
78 
79 
So 
81 

344356 
342035 

339713 
337392 
335071 

I 

* 

118 
119 
1  20 

121 
122 

•  292764 
290571 
288420 
286271 
284121 

Tf 

A 

l 

A 
5 

6 

8 

412113 
409675 
407237 

404800 

402362 
399965 
397568 

395'72 

o 

A 

82 
83 
84 
85 

351406 
348043 
346678 
344356 

12' 

121 
126 

292764 
290571 
288420 
286271 

9 

407722 

86 

87 
88 
89 
90 

92 
93 

342035 
339713 
337392 
335071 
332793 
33°5r4 
328235 

325957 

1 

fa 

13 

129 
130 

'32 

«33 

284121 
281970 
279821 

275606 
273500 
271392 
269286 

O* 

*. 

IO 

ii 

12 
13 
14 
15 
ID 

405274 
402825 
400377 
397928 
395480 

393031 
390624 

1 

A 

50 

52 
53 
54 
55 

351406 

348043 
346678 

344356 
342035 

339713 

1 

P* 

J 

94 

323070 

'33 

137 
138 
139 
140 

265156 
263092 
261028 
258963 
256943 

ror  all  values  o 

17 

18 
'9 

20 
21 
22 

23 
24 

400377 
397928 
39548o 

393031 
390624 

385810 

PI 

ro 

A 

% 

§ 

61 
62 

346678 
344356 
342035 
339713 
337392 
335071 

in 
in 

ft 

9 

97 
98 

99 

IOO 

332793 
330514 
328235 

325957 
323678 
321442 

IOI 

1  02 

03 
04 

319206 
316971 

3r4735 
312500 

00 

,„ 

x  below  jr=6i, 
a  uniformly  dis- 
tributed load  ol 
2700  Ibs.  per  ft. 
will  give  greater 

2  ^ 
26 
27 

380995 
378630 
376264 

64 

344356 
342035 

67 
68 
69 

3397  '3 
337392 
335071 
332793 
3305M 

in 

CO 

/a 

07 
08 
09 

308113 
305921 
303730 
301535 

moments  than 
this  table. 

28 
29 
30 
3' 

385810 
383402 
380995 
378630 

32 

376264 

O 

373897 

m 

A 

70 

339713 

IO 

310307 

34 

\B" 

71 

337392 

II 

308113 

369165 

72 

335071 

o 

12 

305921 

0 

36 

366843 

73 

332793 

in 

ft 

'3 

303730 

, 

37 

364516 

74 
75 

3305M 
328235 

^ 

15 

301535 
299343 

i 

38 

362192 

76 

325957 

16 

297150 

17 

294957 

CONCENTRATED   LOAD  SYSTEM. 


xlix 


MOMENTS. 


=  Rx  —  m. 


SPAN, 

SPAN, 

SPAN, 

SPA.V, 

290 

290 

290 

300 

feet. 

feet. 

feet. 

feet. 

X 

R 

m 

X 

A' 

m 

X 

A5 

m 

X 

A' 

m 

39 
40 

37I53I 
369'65 

77 
78 

355260 
352977 

R 

118 

"9 

301655 

I 
2 

422463 
420026 

41 

366843 

79 

350694 

g 

. 

120 

299537 

o 

^ 

417590 

42 
43 

364516 
362192 

g 

80 
81 

348411 
346128 

"i 

VO 

121 
122 

297420 
295302 

10 

T 

*» 

4 

S 

4'5'53 
412716 

o 

A 

44 

359868 

§1 

t 

82 

343793 

12  5 

293185 

6S 

6 

410320 

45 

357543 

gN 

Pt 

'24 

29ro67 

7 

407923 

46 

355260 

«" 

125 

288950 

8 

405526 

47 

352977 

83 

359868 

* 

48 

350694 

84 

357543 

49 

50 

348411 
346128 

85 
86 

355260 

352977 

126 
'27 

297420 
295302 

9 

10 

418080 
415633 

87 

350694 

o 

128 

293185 

ii 

413226 

88 

34841  i 

8 

r»U 

129 

291067 

12 

410820 

g 

5' 

359868 

89 

346128 

'30 

288950 

_ 

13 

408413 

g 

f* 

357543 

O 

90 

343793 

'3' 

286832 

g 

'4 

406006 

M 

53 
54 

355260 
352977 

§ 

A 

9' 
92 

341509 
339226 

I32 
133 

284715 
282597 

o" 

Pu 

403600 

55 

350694 

- 

93 

336943 

"34 

280480 

56 

348411 

I3S 

278402 

130 

276326 

17 

410820 

94 

346128 

'37 

274250 

18 

408413 

P 

357543 
355260 

9 

343793 
341509 

130 

272174 

'9 

20 

406006 
403600 

59 
60 
61 

62 
63 

352977 
350694 
348411 
346128 
343793 

1 

Pi 

97 
98 

99 

IOO 
IOI 

339226 

336943 
33466o 
332418 
330177 

§ 

•b,. 

'39 
140 
141 
142 

284715 
282597 
280480 
278402 

o 

fill 

21 

22 
23 
24 
25 

401233 
398866 
396500 

394'33  , 
391766 

to 

Pi 

102 

327935 

'43 

276326 

26 

389400 

'03 

325693 

oo 

144 

274250 

" 

27 

387033 

64 

352977 

104 

323452 

'45 

272174 

% 

67 
68 
69 

350694 
348411 
346128 
343793 
341509 

3275000 

ft 

!o6 
107 
108 
109 

321251 
319051 
316851 
314651 

3'245r 

For  all  values  of 
x  below  x  =  51  , 
a  uniformly  dis- 
tributed load  of 

28 
29 

3° 
31 

396500 

394'33 
391766 
389400 

2700  Ibs.  per  ft. 
will  give  greater 
moments  than 

33 

34 

387033 
384666 
382300 

1 

P* 

70 

350694 

no 

321251 

7' 
72 

348411 
346128 

g 

III 

112 

319051 
316851 

0, 

this  table. 

9 

379933 
377606 

73 

343793 

Jo 

Po 

"3 

3'465' 

¥ 

fa 

375280 

74 

341509 

cT 

"4 

3I2451 

ON 

38 

372953 

75 

339226 

* 

115 

310290 

76 

336943 

116 

308131 

"7 

305972  . 

APPENDIX. 


MOMENTS. 


Mx  =  JRx  —  m. 


T 



, 

SPAN, 

SPAN, 

SPAN, 

300 

300 

300 

feet. 

feet. 

feet. 

X 

R 

m 

jr 

R 

• 

m 

X 

R 

m 

39 
40 

382300 
379933 

78 
79 

363/26 
361440 

»9 

120 

310606 

42 

3776o6 
375280 

So 
81 

359'53 
356866 

to 

Ao 

121 

122 

308480 
306353 

1 

A3 

43 
44 

372953 
370626 

§ 

•f> 

82 
83 

354620 
352373 

10 

I23 

124 

304226  . 
302100 

1 

45 

368300 

i? 

Ps 

125 

300013 

46 

366013 

M 

* 

47 
48 
49 
5° 

363726 
361440 

359153 
356866 

84 
85 
86 
87 

368300 
366013 
363726 
361440 

126 
127 
128 

308480 

306353 
304226 

88 
89 

359  '53 
356866 

§ 

129 

302100 
300013 

5' 

370626 

90 

354620 

8 

A. 

131 

297926 

52 

368300 

o 

9i 

352373 

(^ 

132 

295840 

§ 

53 
54 

366013 
363726 

1 

A 

92 
93 

350126 
347880 

'33 
>34 

293753 
291666 

r^ 

A4 

55 

361440 

« 

94 

345633 

'35 

289620 

O 

56 

359153 

95 

343426 

136 

287573 

96 

341220 

'3l 

285526 

138 

283480 

57 

368300 

'39 

281433 

58 

366013 

97 

350126 

140 

279386 

i 

361440 

§ 

fj 

98 
99 

347880 
345633 

141 

277340 

61 

359153 

io 

IOO 

343426 

62 

356866 

IOI 

341220 

o 

142 

289620 

63 

354620 

1  02 

103 

339013 
336806 

w 

fa 

'43 
144 

287573 
285526 

0 

104 

334600 

oo 

'45 

283480 

9 

64 

363726 

105 

332393 

146 

281433 

oo 

As 

a 

361440 
359'  53 

§ 

1  06 

330186 
327980 

147 
148 

279386 
277340 

- 

67 

356866 

Si 

ft 

108 

325773 

'49 

275293 

68 

354620 

r*% 
w 

69 

352373 

ro 

70 

350126 

109 

3346oo 

§ 

no 
III 

332393 
330186 

'50 

283480 

N 

f~) 

A6 

71 

359:53 

112 

327980 

0 

M 

72 
73 
74 
75 
76 

356866 
354620 

352373 
350126 
347880 

! 

ft 

114 
"1 

116 
117 

325773 
323566 
321400 

319233 
317066 

o\ 

A3 

For  all  values  of 
x  below  JT  =  45, 
a  uniformly  dis- 
tributed load  of 

77 

345633 

118 

314900 

2700  Ibs.  per  ft. 

will  give  greater 

moments  than 

this  table. 

CONCENTRATED  LOAD  SYSTEM. 


UK          VSITY 


ILLUSTRATION  OF  THE  USE  OF  THE  TABLES. 


A  FEW  illustrations  will  make  clear  the  use  of  the  tables. 

ist,  SINGLE  SYSTEM  OF  BRACING. — Take,  for  instance,  the  Pratt  truss,  worked  out  on 
p.  107,  Fig.  99.  Here  we  have  /  =  90  feet  required  to  find  the  maximum  strains  due  to 
live  load. 

For  any  upper  flange,  as  A,  Table  II.  for  span  90  feet,  p.  xxii.,  gives  at  once  the 
greatest  moment.  Thus,  since  the  centre  of  moments  for  A  is  at  the  foot  of  the  post  ab,  we 
must  find  the  maximum  moment  at  ten  feet  from  the  left  end.  For  this  point,  the  table 

gives  at  once, 

Maximum  moment  =  Rx  —  m  =  157888  X  10  —  125000  =  1453880; 

dividing  this  by  lever  arm  of  A,  which  is  10  feet,  we  have  at  once, 

A  =  145388  pounds  =  72.69  tons. 
In  like  manner,  for  E,  we  have  ^  =  40 ;  and  hence 

E  X  10  =  Rx  —  m  =  145610  X  40  —  2550000  =  3274400; 
hence 

E  =  327440  pounds  =  163.72  tons. 

So  for  any  flange,  upper  or  lower,  the  greatest  strain  due  to  such  a  rolling  load  as  our  tables 
assume  can  be  at  once  and  easily  found.  This  rolling  load  is  believed  to  be  such  as  to  give 
greater  strains  than  can  ever  occur  in  practice.  To  the  strains  thus  found,  we  must,  of 
course,  add  the  strains  due  to  dead  load.  If  we  assume  this  at  0.5  ton  per  foot,  or  5  tons  at 
each  upper  apex,  as  on  p.  107,  we  have  at  once  for  A,  since  the  re-action  at  left  is  20  tons, 

A  X  10  =  20  X  10,  or  A  '•=  20  tons ; 

E  x  10  =  20  x  40  —  5  (30  +  20  +  10),  or  E  =  50  tons. 

The  total  strains  are,  therefore, 

A  =    72.69  +  20  =  92.69  tons ; 

E  =  163.72  +  50  =  213.72  tons. 

Comparing  these  with  the  strains  found  on  p.  107,  viz.,  A  =  100.33,  ar>d  E  —  223>  tons, 

;  we  see  that  the  method  given  there  gives  us  greater  strains  than  our  table.     This  would 

indicate  that  our  "locomotive  excess  "  of  33  tons,  there  adopted,  is  somewhat  large,  and  that 

*  28  tons  would  nearer  meet  the  requirements  of  practice,  and  cause  the  values  of  p.  107  and 

i  those  found  by  use  of  the  table  to  agree  quite  closely. 

For  any  diagonal,  zsfg;  we  can  easily  find  the  requisite  shear  from  Table  I.  Thus,  we 
have,  in  present  case,  /  =  90,  x  —  40,  /  —  x  —  50,  /  —  x  +  8  =  58.  We  see  at  once,  from 


Ill  APPENDIX. 

Table  I.,  p.  iii.,  that  the  limit  for  span  90  feet  is  48^ ;  hence,  for  x  =  40,  we  must  use 
formula  II.  We  have,  then, 

115000  „      1715000          3210000 

Shear  =  — 58  -} — — 50  —  ^— 15000  =  56222  =  28.1  tons. 

90    •  90  90 

To  this  add  the  dead-load  shear,  which  is  5  tons,  and  we  have  shear  for  fg  33.  i  tons.  The 
shear  found  on  p.  108,  for  33  tons  locomotive  excess,  is  40  tons.  As  before  remarked,  the 
results  there  given  are  somewhat  large,  and  a  locomotive  excess  of  28  tons  would  give  a 
closer  agreement. 

The  preceding,  if  followed  carefully,  will  fully  explain  the  use  of  our  tables  in  all  cases 
where  we  have  but  a  single  system  of  bracing. 

2d,  DOUBLE,  OR  MULTIPLE,  SYSTEM.  —  For  any  flange,  find  from  Table  II.  the  greatest 
moment  for  its  nearest  centre  of  moments,  and  then  find  what  uniform  load  will  give  this 
same  moment  at  the  same  point ;  calculate  the  flange  for  this  uniform  load  divided  into 
apex  loads,  and  acting  upon  each  system. 

If  x  is  the  distance  from  left  end  to  centre  of  moments,  and  p  is  the  uniform  load  per 

unit  of  length,  then  — (/  —  x)  is  the  moment.     Put  this  equal  to  the  moment  found  from 

Table  II.,  and  the  value  of  /  can  be  found,  in  pounds  per  foot,  which  would  give  the  same 
moment  as  the  table,  at  the  given  point.  The  flange  can  then  be  calculated  for  this  uniform 
load.  Each  flange  should  thus  be  calculated  for  its  own  equivalent  uniform  load. 

For  any  brace,  find  the  greatest  shear  at  the  foot  of  it  from  Table  II. ;  then  find  the 
equivalent  uniform  moving  load  ;  divide  this  into  apex  weights,  and  calculate  the  brace  for 
this  loading. 

If  m  is  the  uniform  moving  load  per  unit  of  length,  coming  on  from  right  and  extending 

my x\z 

up  to  a  distance  of  x  from  the  left  end,  then  the  shear  is  — - — -. • 

2/ 

Put  this  equal  to  the  shear  found  from  Table  II.,  and  the  value  of  m  can  be  found  in 
pounds  per  foot,  which  would  give  the  same  shear  as  the  table.  The  brace  can  then  be 
calculated  for  this  uniform  moving  load.  Each  brace  should  thus  be  calculated  for  its  own 
equivalent  uniform  load. 


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